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ELEMENTS    OF 


DEDUCTIVE   LOGIC 


BY 

NOAH  K.  DAVIS,  Ph.D.,  LL.D. 

iir 
PROFESSOR  OF  MORAL  PHILOSOPHY  IN  THE  UNIVERSITY  OF  VIRGINIA 
AND    AUTHOR    OF  "  THE  THEORY  OP    THOUGHT  "    "  ELE- 
MENTS  OF   INDUCTIVE   LOGIC  "  ETC. 


Xpljatfiof  h  wpayaareia  wpdt  yvuvaaiav,  wpot  rut  Ivrev^eit 
npot  rat  Kara  ipi\oao<piav  ijrtarijfiat. — Aristotlb 


NEW  YORK  •:•  CINCINNATI  •:•  CHICAGO 

AMEKICAN     BOOK     COMPANY 


Copyright,  189B,  by  Harfxb  &  Brothxrs. 


^11  rights  reterved. 
W.  P.   2 


ii'^T-a 


PREFACE 


This  treatise  is  designed  as  a  text-book  for  under- 
graduates. It  comprises  the  body  of  approved  log- 
ical doctrine,  so  that  in  a  limited  time  a  student 
may  acquire  a  rounded  knowledge  of  the  funda- 
mental forms  jjf  thought,  be  profited  by  the  excel- 
lent discipline  of  the  study,  and  prepared  for  the 
psrsuit  of  philosophical  sciences. 

Those  who  wish  to  go  beyond  the  elements  of 
logic  will  find  much  additional  matter  in  my  larger 
work,  entitled  "  The  Theory  of  Thought,"  designed 
especially  for  universities.  In  my  "Elements  of 
Psychology  "  are  explained  the  relation  of  the  idea 
as  a  mental  image  to  the  notion  as  a  product  of 
thought,  and  the  various  mental  processes  involved 
in  thinking.  In  both  works  many  references  will 
be  found  to  authorities  and  to  the  literature  of  the 
subject. 

In  the  preparation  of  the  present  text,  I  have 
tried  to  be  clear,  simple,  and  true,  and  to  mitigate 
the  natural  severity  of  the  subject  by  copious  illus- 
tration.   The  care  I  have  taken,  and  my  experience 


IV  PREFACE 

of  more  than  twenty  years  in  teaching  logic,  lead 
me  to  hope  that  my  fellow-teachers  and  their  pupils 
will  find  the  treatise  well  adapted  to  their  wants, 
and  that  it  will  therefore  tend  to  promote  the  study 
of  this  admirable  and  invaluable  science. 

A  special  feature  is  a  praxis  appended  to  each 
chapter.  Many  standard  exercises  have  been  re- 
tained, and  many  new  ones  introduced.  They  have 
been  carefully  arranged  in  progressive  order,  in  cor- 
respondence with  the  increasing  complexity  of  the 
subject,  1  would  suggest  that  the  working  of  the 
praxes  alone,  wjthout  any  recitation  of  the  text, 
will  insure  a  more  satisfactory  knowledge  of  ele- 
nientary  logic  than  the  closest  reproduction  of  the 
text,  the_praxes  being  omitted. 

In  the  chapter  on  Fallacies,  I  have  adhered  to  the 
original  Aristotelic  distribution,  believing  that  it 
should  be  well  known  to  every  student  of  logic,  and 
that  none  better  has  been  proposed. 

No  treatment  of  induction  is  included  in  this 
book.  But,  deeply  impressed  with  the  importance 
of  that  branch  of  logic,  especially  in  its  relation  to 
the  physical  sciences,  I  have  prepared  a  companion 
volume,  entitled  Elements  of  Inductive  Logic,  which 
completes  the  system. 

Noah  K.  Davis. 
UNivKRsrrY  OP  Vikginia. 


CONTENTS 


INTRODUCTION 

I.— DEFINITION  OF   LOGIC 

Page 

§  1.  The  definition.     The  word.     A  valued  study 1 

§  2.  Science  distinguished  from  art.     Logic  a  science 1 

§  3.  Thought  the  object-matter  of  logic 3 

§  4.  Forms  of  thought.     Second  intentions 4 

§  5.  Necessity  of  the  forms.    Their  violability 5 

§  6.  Free  treatment  adopted 6 

II.— PRIMARY   LAWS 

§  7.  Their  origin  and  general  character 8 

§  8.  The  Law  of  Identity.     Rhetorical  forms 9 

§  9.  The  Law  of  Contradiction.     Rhetorical  forms 9 

§  10.  The  Law  of  Excluded  Middle 11 

§  11.  Single  statements.     Co-ordinate  and  complementary. .  11 

§  12.  Logic  only  a  negative  criterion  of  reality 13 

§  13.  The  postulate  of  logic.     EquipoUence 13 

§  14.  Praxis  on  Primary  Laws 14 


PART  I.— CONCEPTION 

I.— THE   NOTION 

§  15.  Abstraction.    Marks.     Concrete  and  abstract  terms. . .  15 

§16.  Generalization.     Classification.     Specialization 17 

§  17.  Conception.    Individual  and  general  concepts 18 

§  18.  These  momenta  coexist.     Mark  and  concept 20 

§  19.  Denomination.     Common  and  proper  names 20 


VI  CONTENTS 

Page 

§  20.  Intension  and  extension  of  concepts.     Correlated 22 

§  21.  Progress  towards  perfection.     Clear  and  distinct 23 

§22.  Praxis  on  The  Notion 25 

II.— RELATIONS 

§  23.  The  qualitative  and  quantitative  wholes 36 

§  24.  The  quantitative  whole,  integral  and  collective 27 

§  25.  The  qualitative  whole,  intensive  and  extensive 28 

§  26.  Coextension  of  notions 30 

§  27.  Subordination  of  notions.     Genera  and  species 30 

§  28.  Praxis  on  Relations 32 

III.— DIVISION 

§  29.  Co-ordination  of  notions.     Dichotomy 33 

§  30.  Negative  notions.     Correlative  notions 34 

§  31.  Trichotomy  and  polytomy.     Disparate  notions 35 

§  32.  The  ground,  process,  and  kinds  of  division 36 

§  33.  Rules  for  division 37 

§  34.  Praxis  on  Division 39 

IV.- DEFINITION 

§  35.  Intensive  view  of  definition.     An  explication  of  marks  41 

§  36.  Indefinable  notions.     Convertibility 41 

§  37.  Extensive  view.     Intersection.     Genus  and  difference.  42 

§  38.  Forms  approximating  definition 43 

§  39.  Kinds  of  definition ;  real,  nominal,  genetic 44 

§  40.  Rules  for  definition 45 

§  41.  Praxis  on  Definition 47 

v.— SYSTEM 

§  42.  Scheme  of  intension  and  extension 49 

§  43.  Scheme  of  first  and  second  intentions 49 

§44.  The  summum  genus.    In  science.    In  talk 50 

§  45.  The  infima  species.     In  nature — not  considered 51 

§  46.  Individuals,  the  basis  but  not  parts  of  a  logical  system  52 
§  47.  Relation  of  division  and  definition  in  a  system 54 


CONTENTS  Vll 

Page 

§  48.  Expression  of  a  system.     Porphyry's  tree 56 

§  49,  Praxis  on  System 57 

VI.— PREDICATION 

§  50.  Its  form  limited  only  by  self-contradiction 59 

§  51.  Quality  of  judgments  or  propositions 59 

§  52.  Existence  predicated.     Relative.     Absolute 60 

§  53.  Negative  forms.     Pure.     Infinite.     Impure 61 

§  54.  Intensive  and  extensive  forms.    A  non-predicable 62 

§  55.  The  categories  of  Aristotle.     Interpreted 63 

§  56.  The  predicables  of  Aristotle 64 

§  57.  Praxis  on  Predication 65 

VII.— SIMPLE   PROPOSITIONS 

^  58.  Propositions  of  two  kinds,  categorical  and  conditional  67 

§  59.  The  categorical  proposition  dissected 68 

§  60.  The  copula,  its  tense,  its  quality.     Negative  subject  or 

predicate 69 

§  61.  Strict  logical  order.     Rhetorical  displacements 70 

§  62.  Quantity  of  judgments  or  propositions 71 

§  63.  Individual  propositions 72 

§  64.  Universal  propositions.     Signs  of.     Ambiguity  of  all ,  73 

§  65.  Partial  or  indefinite  propositions.     Signs  of 73 

§  66.  Ambiguity  of  some.     Its  semi-definite  sense 74 

§  67.  Scheme  of  the  prepositional  forms 75 

§  68.  Complex  propositions.  Subdivision.  Treated  as  simple  75 

§  69.  Praxis  on  Simple  Propositions 77 

VIII.— COMPOUND   PROPOSITIONS 

§  70.  First  kind,  having  components  obvious 79 

§71.  Second  kind,  exponibles.    Exclusives  and  exceptives .  79 

§  72.  Semi-definite  propositions 81 

§  73.  Quantified  predication.    Small  letter  symbols 82 

§  74.  Two  views;  compound  qualitative,  or  simple  quantita- 
tive   83 

§  75.  Rule  for  quantifying  the  predicate 85 

§  76.  Praxis  on  Compound  Propositions 85 


VJll  CONTENTS 


PART  IL— DEDUCTION 

I.— IMMEDIATE   INFERENCE 

I'agc 

§  77.  Definition  and  distribution  of  judgments 87 

§  78.  Implications  distinguished  from  inferences 88 

§  79.  Rule  limiting  quantification.    Illicit  procesa 89 

§  80.  Determination.     Modified  forms  of 90 

§  81.  Infinitation.    Rule  for 91 

§  82.  Conversion.     Three  kinds  of.     Remarks 91 

§83.  Opposition.     Square  of.     Rules.     Table  of  relations.  94 

§  84.  Praxis  on  Immediate  Inference 97 

II.— THE  SYLLOGISM 

§85.  Reasoning  and  the  syllogism  illustrated  and  defined. .  99 
§  86.  Dissection  of  the  syllogism.    Its  parts  defined.    Their 

order 100 

§  87.  Notations,  circular  and  linear,  disapproved  ;  graphic, 

approved 102 

§  88.  Intensive  and  extensive  forms.    Rule  for  converting.  104 

§  89.  This  distinction  examined,  and  discarded 105 

§  90.  The  syllogistic  judgment.     Characterized  by  neces- 
sity   107 

§  91.  Relative  truth  or  falsity  of  its  several  propositions. . .  108 

§  92.  Praxis  on  The  Syllogism 109 

III.— CANON  AND   RULES 

§  93.  The  canon.     Four  forms  of,  with  comments Ill 

§  94.  The  eight  general  rules,  with  reasons  and  comments. .  114 
§  95.  Praxis  on  Canon  and  Rules 113 

IV.— FIGURE   AND   MOOD 

§  96.  The  four  figures  explained  and  illustrated 120 

§  97.  Special  rules  relative  to  the  several  figures 121 

§  98.  The  nineteen  moods,  how  ascertained 12S 


CONTENTS  IX 

Pago 
§  99.  Names  of  the  moods.     Two  basic  fonns.    The  con- 
clusions    123 

§  100.  Reduction,  ostensive.     How  accomplished.    General 

rule 125 

§  101.  Reduction,  indirect.    How  accomplished.     Superflu- 
ous    127 

§  102.  The  fourth  figure  criticised.     Superfluous  and  erro- 
neous    128 

%  103.  Praxis  on  Figure  and  Mood 129 

v.— MODIFIED  FORMS 

§  104.  The  enthymeme.    Its  four  orders  illustrated 132 

§  105.  The  epichirema.     Defined  and  illustrated 134 

§  106.  The  sorites.     Its  two  forms.     Five  points  noted. . . .  134 
§  107.  Compound  and  irregular  syllogisms,  with  illustra- 
tions   136 

§  108.  Seven  methods  of  argumentation.   Remarks 139 

§  109.  Praxis  on  Modified  Forms 142 

VI.— CONDITIONAL  PROPOSITIONS 

§  110.  Conditions,  three  kinds — real,  causal,  logical 146 

§  111.  General  distribution  of  propositions 147 

§  112.  The  conjunctive  proposition.     Forms  of 148 

§  113.  The  disjunctive.     Contradictory  forms  of 149 

§  114.  The  disjunctive.     Modified  forms  of 150 

§115.  The  conjunctivo-disjunctive.     Forms  of 152 

§  116.  Interpretation  of  the  conjunctive  judgment 153 

§  117.  Praxis  on  Conditional  Propositions 155 

VII.— CONDITIONAL  SYLLOGISMS 

§  118.  Reasonings  founded  on  conditional  forms 158 

§119.  The  conjunctive  syllogism;  axioms,  moods,  rules. .. .  159 
§  120.  The  disjunctive;  contradictory,  subcontrary,  and  cop- 
ulative    161 

§  121.  The  conjunctivo-disjunctive;  double  treatment 163 

§  122.  The  dilemma;  simple  and  complex  forms 163 

§  123.  Criticism  and  estimate  of  the  forms 165 

§  124.  Praxis  on  Conditional  Syllogisms 168 


CONTENTS 


VIII.— QUANTITATIVE  FORMS 

Page 

§125.  The  quantitative  whole.     Kind  and  degree 171 

§  126.  Quantitative  notions,  common  and  proper 171 

§  127.  Judgments  of  equality  and  inequality 172 

§  128.  Immediate  inference 174 

§  129.  Mediate  inference.     Syllogisms  of  equivalence 175 

§  130.  Geometrical  illustration.     Its  generality 177 

§131.  Mediate  inference.     Syllogisms  of  inequality 178 

§  132.  Praxis  on  Quantitative  Forms 180 

IX.— FALLACIES 

§  133.  Definition.     Two  remarks.    Distribution 183 

§134.  Paralogisms.    Apparent  violations 184 

§  135.  Sophisms  in  diction — ambiguities 185 

§  136.  ^quivocatio.     Its  importance.     Jests 185 

§  137.  Amphibolia.     The  oracles 186 

§138.  Compositio  et  divisio.   Another  view.    Punctuation..  187 

%  139.  Accentus,  prosodia.     Sarcasm 188 

g  140.  Figura  dictionis.     Solecisms  and  paronyms 189 

§  141.  Sophisms  in  matter.     Meaning  of  this  title 190 

§  142.  Accidens.     Illustrations    190 

§  143.  Secundum  quid.    Two  forms  of 191 

§144.  Ignoratio  elenchi.     Enlarged  view  of 192 

§  145.  Consequens.     Two  forms  of 193 

§  146.  Petitio  principii.     Five  forms  of 194 

§  147.  Noa  causa  pro  causa.     An  erroneous  view  of 196 

§  148.  Plures  interrogationes,  or  cornutus.    Varietiea  of . . .  197 

§  149.  Praxis  on  Fallacies 198 

Index 205 


ELEMENTS    OF 
DEDUCTIVE   LOGIC 


INTRODUCTION 
I.— DEFINITION  OF  LOGIC 

§  L.  Logic  is  the  science  of  the  necessary 
tbrms  of  thought.  The  word  logic  is  Greek, 
Aristotle,  the  author  and  finisher  of  the  science, 
did  not  give  this  name  to  his  work,  but  it  was  ap- 
pUed  by  his  followers,  and  has  been  for  many  cen- 
turies its  universally  recognized  title.  In  the  me- 
diasval  universities,  logic  was  studied  as  one  of  three 
ways  to  eloquence,  and  in  modern  schools  it  is  just- 
ly held  in  high  esteem  as  an  independent  science 
and  an  excellent  discipline. 

It  will  be  well,  at  the  outset,  to  have  a  distinct 
explication  of  the  several  terms  used  in  the  forego- 
ing definition  of  logic,  and  to  this  we  now  proceed. 

§  2.  A  science  is  a  complement  of  knowledge 
having,  as  to  form,  the  character  of  logical  perfec- 
tion: as  to  matter,  the  character  of  truth.  Lot;- 
ical  perfection  requires  primarily  that  the  oi)jects 

1 

.     / 


3  INTRODUCTION 

of  knowledge  shall  be  classified  clearly,  distinctly, 
completely,  and  harmoniously.  Truth  requires  that 
the  objects  be  real ;  what  is  unreal  and  false  cannot 
constitute  a  science.  Hence,  a  science  is  a  perfect- 
ed system  of  truths;  or,  science  is  classified  knowl- 
edge. Few  branches  have  reached  this  ideal  per- 
fection ;  perhaps  pure  mathematics  alone  has  done 
so;  but  others,  having  made  high  attainments,  are 
properly  called  sciences. 

Science  and  art  should  be  distinguished.  A  sci- 
ence  teaches  us  to  know,  an  art  to  do.  Science 
discovers  laws,  art  gives  rules.  Science  is  specu- 
lative, art  practical.  The  scientist  knows  the  prop- 
er relations  of  things,  the  artisan  brings  them  into 
these  relations.  There  is  a  science  of  civil  law, 
there  is  an  art  for  the  practitioner.  Anatomy  is  a 
science,  surgery  an  art.  But  science  often  leads 
so  directly  to  art,  and  art  is  so  dependent  on  sci- 
ence, that  they  are  not  always  clearly  distinguish- 
able. 

Now,  logic  is  not  at  all  an  art,  but  strictly  a  sci- 
ence. It  tells  us  how  we  think  when  we  think  cor- 
rectly, but  does  not  pretend  to  tell  us  how  to  think. 
It  is  of  great  interest  to  know  what  are  the  princi 
pies  and  processes  of  thought,  the  laws  that  regulate 
intellect  in  the  attainment  of  truth .  Yet  knowl- 
edge is  power,  and  when  one  has  mastered  this  sci- 
ence there  is  a  practical  result  in  a  special  cultiva- 
tion of  his  faculties ;  for  whatever  process  one  clear- 
ly understands,  it  is  manifest  he  can  more  eiRciently 
perform.     As  grammar  and  rhetoric  are  helpful  to 


DEFINITION   OF    LOGIC  3 

correct  and  elegant  speaking  and  writing,  so  logic 
is  helpful  to  correct  and  cogent  thinking. 

§  3.  The  object-matter  of  logic  is  thought.  Each 
science  has  its  own  object-matter.  As  a,stronomj 
treats  of  Jhe  stars,  geology  of  the  earth's  crust,  zo- 
ology of  its  fauna,  botany  of  its  flora,  mathemat- 
ics of  quantity,  theology  of  God.  philosophy  of  prin- 
ciples, psychology  of  mind,  ethics  of  morals,  so  logic 
treats  of  thought.  Thought  denotes  the  acts  of  the 
understanding  as  distinguished  from  perception, 
memory,  imagination,  feeling,  desire,  and  volition, 
of  whose  exercises  logic  takes  no  notice.  Thought 
is  the  bringing  a  notion  into  or  under  anothei:^ 
This  is  to  comprehend  or  understand  it.  For  ex- 
ample, when  I  say  a  lily  is  a  flower,  I  bring  myi 
notion  lily  under  a  class-notion  flower,  and  so  this] 
is  a  thought.  Now,  we  think  about  all  kinds  of 
things,  but  logic  is  indifferent  to  all  except  one — 
that  is,  thought  itself.  In  studying  logic,  we  think 
about  thought.  As  a  science,  it  is  the  theory  of 
thought. 

Let  it  not  be  supposed,  however,  that  logic  treats 
of  thought  as  exercised  in  scientific  pursuits  only. 
It  treats  of  thought  universally.  Thought  as  found 
in  all  sorts  of  litemture  and  speech,  in  common 
conversation,  in  silent  meditation,  all  our  everyday 
thinking  about  the  most  trivial  things  at  any  in- 
stant, as  well  as  the  lofty  thought  of  the  philoso- 
pher or  theologian,  is  of  the  same  nature,  proceeds 
in  the  same  manner,  is  according  to  the  same  laws,  js 


4  INTKODUCnON 

logical  if  correct.     Logic  explains  how  any  human 
mind  thinks  correctly  at  any  time  about  any  thing. 

§  4.  It  appears,  then,  that  logic  has  nothing  to 
do  with  the  things  we  think  about.  It  treats  of 
thought  in  disregard  of  its  conten);.  Excluding  the 
matter  of  thought,  it  discusses  the  form  of  thought. 
The  form  as  distinguished  from  the  matter  may  be 
exemplified  thus :  When  I  think  that  the  book  be- 
fore me  is  a  folio,  the  matter  of  this  thought  is 
book  and  folio,  the  form  is  a  judgment.  Thought 
is  concerned  with  the  relations  of  objects  to  each 
other,  and  the  nomenclature  of  logic  consists  of  the 
names  of  these  relations  apart  from  the  objects  re- 
lated ;  as,  judgment,  concept  and  mark,  species  and 
genus,  subject  and  predicate,  definition,  syllogism, 
dilemma,  etc.  These  are  all  names  of  mere  forms 
of  thought. 

In  medicieval  logic,  the  matter  and  form  were  dis- 
tinguished as  first  and  second  intentions.  First  in- 
tentions are  names  of  objects;  as,  lily  and  flower, 
book  and  folio.  Second  intentions  are  names  of 
relations ;  as,  species  and  genus.  Hence  a  second 
intention  is,  in  modern  logic,  a  form  of  thought. 
Logic,  then,  is  ajcience  of  second  intentions.  Gram- 
mar, also,  is  a  science  of  second  intentions,  treating 
of  the  forms  of  speech  ;  as,  verb,  adverb,  noun,  ad- 
jective, clause,  sentence,  etc.  Grammar  is  the  sci- 
ence of  second  intentions  or  forms  of  speech.  Log- 
ic_is  the  science  of  second  intentions  or  forms  of 
thoufirht. 


DEFINITION    OF  I-OGIC  O 

The  matter  and  the  form  of  thought  cannot  have 
any  actually  separate  existence.  JS'o  object  is  think- 
able except  under  some  form  of  thought ;  no  form 
of  thought  can  have  any  existence  in  consciousness 
unless  there  be  some  object  of  thought.  But  by 
abstraction  we  can  contemplate  these  apart;  we 
can  consider  either  the  object  of  thought  or  the 
manner  of  thinking  it ;  we  can  distinguish  the  form 
from  the  content  or  matter.  LiOgic,  therefore,  is  ap 
abstract  science,  abstracting  from  all  matter  the 
mere  form  of  thought,  and  considering  this  only. 

It  follows  that  logic  stands  in  a  similar  and  fun- 
damental relation  to  all  other  sciences,  for  it  consid- 
ers only  what  is  common  to  all — that  is,  the  forms 
of  thought  to  which  all  are  subjected — making  that 
alone  its  object-matter.  Now,  philosophy  is  the  sci- 
ence of  principles,  and  therefore  fundamental  in 
treating  of  the  primary  truths  that  underlie  all 
knowledge.  But  philosophy  proceeds  logically  or 
not  at  all.  Hence  logic  is  fundamental  even  t@  phi- 
losophy, in  that  it  exhibits  the  processes  of  thought 
which  bind  philosophy  as  well  as  all  othei  sciences. 
Moreover,  logic  itself  must  proceed  logically,  and 
can  become  a  science  only  by  conforming  to  those 
laws  which  it  is  its  province  to  explicate  and  ex- 
hibit. 

§  5.  Logical  forms  are  necessary  forms.  That  is 
to  say,  the  mind  cannot  think  truly,  unless  it  pro- 
ceed according  to  these  forms.  It  must  not  be 
understood  that  logic  invents  laws  to  control  our 


6  INTRODUCTION 

thinking ;  it  merely  discovers  and  unfolds  the  strict 
necessities  that  exist  in  the  very  nature  of  mind  and 
things,  and  formulates  them  as  laws  of  thought.  It 
demonstrates  that  the  mind  must  proceed  accord- 
ing to  these  laws  or  under  these  forms,  if  the  pro- 
cess be  truly  consecutive  from  one  thought  to  an- 
other. Any  violation  of  the  laws,  or  deviation  from 
the  forms,  it  shows  to  be  an  inconsequence,  and 
therefore  futile. 

For  these  laws  are  not  necessary  in  the  sense  that 
they  are  inviolable.  We  may  wilfully  or  ignorantly 
disregard  them ;  and,  blinded  by  prejudice  or  pas- 
sion or  confusion  of  thoughts,  we  often  do  violate 
them  ;  but  the  process  is  fallacy  and  error,  and  the 
result  null  ;ind  void.  All  consequent  thinking  must 
be  legitimate ;  that  is,  it  necessarily  conforms,  con- 
sciously or  unconsciously,  to  these  laws.  The  con- 
formity is  necessary  to  valid  thought.  This  is  log- 
ical necessity  (not  unlike  the  practical  necessity  of 
a  certain  means  to  a  certain  end),  and  should  be  dis- 
tinguished from  philosophical  necessity  and  moral 
necessity. 

§  6.  Such,  then,  is  the  definition  of  Pure  Logic, 
both  Deductive  and  Inductive.  Since  it  excludes 
the  matter  of  thought,  considering  only  its  form,  a 
strict  observance  of  its  limits  w^ould  forbid  the  use 
of  concrete  examples.  This  would  make  the  treat- 
ment very  narrow,  dry,  and  difficult.  We  shall 
therefore  transgress  the  bounds  of  the  definition 
whenever  it  seems  desirable,  and  give  concrete  illus- 


DEFINITION   OF   LOGIC 


trations  involving  matter,  hoping  to  enliven  and 
facilitate  the  study.  The  student,  however,  should 
constantly  keep  in  mind  that  logic  has  nothing  to 
do  with  the  matters  thought  about,  does  not  at  all 
concern  itself  with  the  truth  or  falsity  of  any  prop- 
ositions used  for  illustration,  but  deals  only  with 
the  forms  in  which  such  matter  is  expressed. 


IL^PRIMARY   LAWS 

§  7.  An  analysis  of  our  thoughts,  discharging 
their  matter,  discovers  that  they  have  definite  forms 
(§  4).  These  forms,  being  native  and  necessary  (§  5), 
are  universal;  that  is,  they  are  in  all  thoughts, 
and  all  thoughts  are  in  them.  Since  they  are  uni- 
versal, we  may  view  them  as  conforming  to  laws ; 
and  these,  when  formulated,  are  known  as  the  laws 
of  logic.  Now,  a  thorough  analysis  of  the  empty 
forms,  rejecting  their  differences,  discloses  certain 
general  abstract  principles.  As  the  result  of  com- 
plete analysis,  these  are  ultimate;  as  essential  in 
every  thought,  even  in  that  of  themselves,  they  are 
necessary;  as  common  to  all  the  forms,  they  are 
strictly  universal ;  as  intuitively  self-evident,  they 
are  axiomatic.  These,  then,  are  called  Logical 
Principles,  or  Primary  Laws  of  Thought. 

This  complement  of  laws  is  assumed  by  logic  as 
its  jpuncturti  saliens,  and  it  proceeds  to  demonstrate 
from  them  as  axioms  the  secondary  and  special 
laws  that  regulate  all  thinking.  The  whole  of  pure 
logic  is  only  an  articulate  development  of  the  pri- 
mary laws  and  of  their  applications.  Deductive 
logic  posits  three  laws;  inductive  logic  superadds 
others. 


PEIMARY    LAWL  9 

§  8.  The  three  primary  laws  are  as  follows: 
The  first  is  the  Law  of  Identity.  It  is  the  princi- 
ple of  affirmation.  It  is  variously  stated,  but  pref- 
erably thus :  Whatever  does  not  contradict  a  / 
subject  may  be  affirmed  of  it.  The  subject 
and  the  attribute  are  thereby  identified ;  hence  the 
name  of  this  law.  E.  g.,  ^  is  ^;  2x3=6 ;  The 
moon  is  our  satellite  ;  Frcmcis  Bacon  is  Lord  Veru- 
lam;  Saltpetre  is  nitrate  of  potassa.  In  these  ex- 
amples the  identity  in  thought  is  entire. 

But  the  law  extends  to  partial  identity.  E.  g,, 
A  is  a  /  6  >  Jf- 1  The  moon  is  spherical  /  Congress  is 
vn  session  /  Silver  is  a  metal.  In  this  case  one  term 
is  only  a  part  of  the  content  of  the  other.  The 
great  majority  of  propositions  take  this  form  (§  50). 

Supplementary  laws  are:  Whatever  is  essential 
iira"sub]ecFiiiusT  be  affirmed  of  it ;  as,  The  sun  is 
bright;  and.  Whatever  is  not  essential  in  a  subject 
may  be  denied  of  it ;  as.  The  sun  is  not  up. 

Strictly  logical  propositions  are  always  to  be  con- 
strued literally,  and  should  be  distinguished  from 
rhetorical  forms,  wherein  more  is  meant  than  meets 
the  ear.  E.  g.,  -4  marCs  a  man  for  a)  that ;  What 
I  have  written  I  ha/ve  written  /  /  am  that  I  am. 
Such  highly  significant  expressions  in  rhetorical 
identity  have  no  meaning  when  taken  literally. 

§  9.  The  second  is  the  Law  ©f  ©©ntrabiction.  It 
is  the  principle  of  negation.  Its  statement  is : 
Whatever  contradicts  a  sub^ject  must  be 
denied  of  it.     lieing  in  opposition,  the  subject 


^ 


10  INTRODUCTION 

and  an  attribute  are  thereby  set  apart.  Contradic- 
tories cannot  coexist ;  afl&rmations  not  self -consist- 
ent are  unintelligible.  If  we  attempt  to  unite  them, 
the  thought  is  null,  it  destroys  itself.  E.  g.,  A  is 
not  A^=0  ;  The  circle  is  square ;  The  larger  half ; 
The  lams  of  chance  ;  I  expected  to  he  dismffinted  ; 
It  is  certain  that  nothing  is  certain.  This  is  the  log- 
ical paradox,  or  logical  absurdity.  Also  notions 
that  are  incongruous,  as  noisy  colors,  are  essentially 
contradictory,  and  cannot  coexist. 

According  to  the  law,  we  must  deny  contradic- 
tories of  each  other.  Of  two  contradictories  one 
must  be  false.  E.  g.,  ^  is  not  norirA  ;  2+3  is  not  4^; 
No  pain  is  pleasurable  /  What  is  wrong  can  never 
he  right ;  JVo  lie  is  of  the  truth.  Let  it  be  observed 
that  A  and  non-A  divide  the  universe  of  things,  so 
that  whatever  is  one  is  not  the  other;  everything 
is  either  man  or  non-man.  Such  opposition  is  abso- 
lute contradiction.  But  the  members  of  a  genus  or 
logical  universe,  though  in  themselves  mere  contra- 
ries, are  contradictory  of  each  other  relatively  to 
their  limiting  genus.  Thus,  if  we  take  the  universe 
animal,  then  everything  within  this  universe  or 
genus  is  either  man  or  non-man,  i.  e.  brute,  and  so 
these  are  contradictories.  E.  g.,  A  mam.  is  not  a 
brute  ;  likewise,  A  fish  is  not  a  reptile  ;  A  whale  is 
not  a  fish ;  A  vine  is  not  a  tree.  For  similar  rea- 
sons, an  attribute  incongruous  to  a  subject  is  to  be 
denied  of  it;  as,  A  dishonest  man  is  not  trust- 
worthy. Likewise  two  individuals  are  denied  of 
each  other ;  as,  Francis  Bacon  is  not  Roger  Ba^on. 


PRIMARY    LAWS  11 

Rhetorical  contradictions  are  often  used  to  con- 
vey emphatically  a  covert  meaning.  E.  g.,  Bitter 
Sweet;  Festina  lente ;  Not  to  decide  is  to  decide; 
When  I  am  weak,  then  am  /  strong  ;  Hope  that  is 
seen  is  not  h(!>pe  /  In  diplomacy,  whatever  is  is  some- 
thing else ;  Learned  ignorance  is  wiser  than  pre- 
sumptuous knowledge.  Such  opposites  are  like  the 
barbs  of  an  arrow.  The  invisible  point  pierces,  the 
barbs  cling.     This  is  the  rhetorical  paradox. 

§  10.  The  third  is  the  Law  of  Excluded  Middle. 
It  prescribes  a  necessity  in  affirmation.  A  state- 
ment is:  Wh^^®'^®^  contradicts  a  contradic- 
tory of  a  subject  must  be  affirmed  of^t^^  Evi- 
dently, of  two  absolute  contradictories  one  must 
be  true  of  any  subject.  If  a  genus  or  logical  uni- 
verse be  strictly  divided  into  two  species,  every- 
thing: within  it  must  be  of  one  or  the  other  kind. 
In  either  case  no  third  affirmation  is  possible,  i.  e., 
every  middle  possibility  is  excluded;  hence  the  name 
of  this  law.  E.  g.,  X  is  either  A  or  non-A  ;  God  ex- 
ists, or  does  not  exist ;  Every  animal  that  is  not  a 
man  is  a  brute;  Defence  being  impracticable,  we 
must  yield  ;  To  be  or  not  to  be,  that  is  the  question  ; 
If  he  do  not  fulfil  the  agreement,  I  shall  be  disap- 
pointed. The  argument  called  reductio  ad  absur- 
dum  {%  108)  is  an  application  of  this  law.  Of  two 
contradictory  alternatives  it  shows  one  to  be  al> 
surd^  hence  the  other  must  be  allowed. 

§  11.  The  second  and  third  laws  are  often  united 


12  INTKODUCTION 

in  one  brief  but  compound  statement ;  as,  Of  two 
contradictories  one  must  be  false,  the  other  true ; 
or,  Any  attribute  must  be  either  denied  or  affirmed 
of  any  subject. 

It  has  been  proposed  to  reduce  the  three  laws  to 
one  simple  statement ;  as,  All  thought  must  be  self- 
consistent.  But  an  analysis  of  self-consistency  will 
evolve  the  three  laws  as  its  ground.  Still  contra- 
diction is  obviously  their  common  principle. 

Also  the  attempt  has  been  made  to  deduce  from 
one  the  other  two.  But  neither  can  be  inferred  as 
a  second  from  another  as  first.  In  every  such  at- 
tempt the  inferred  law  is  necessarily  presupposed, 
4  L  which  is  petitio  principii.  Like  the  sides  of  a  tri- 
angle, not  only  are  they  not  the  same,  not  reduci- 
ble to  unity,  but  also  each  gives,  in  its  own  exist- 
ence, the  existence  of  the  other  two.  The  three 
are  co-ordinate  and  complementary ,  dis^inpt.  y^t- 
inseparable. 

§  12.  It  has  already  been  said  that  logic  is  con- 
cerned only  with  the  form,  not  at  all  with  the  mat- 
^  ter,  of  thought.  Consequently,  it  furnishes  no  guar- 
antee or  criterion  of  the  material  truth  of  any 
proposition.  There  is  no  logical  fault  in  our  say- 
ing, for  instance,  that  Spain  is  an  island,  or  that 
Theft  \^  justifiable.  These  false  affirmations  are  in 
accord  with  the  first  law,  and  so  are  formally  cor- 
rect. What  is  conceivable  in  thought  may  be  quite 
impossible  in  fact,  and  so  is  merely  logically  possi- 
ble ;  as,  a  centaur.     For  the  sphere  of  thought  is 


PKIMAKY    LAWS  13 

far  wider  than  the  sphere  of  reality,  and  there  is 
no  valid  inference  from  the  correctest  thinking  a 
thing  to  its  actual  existence. 

But  whatever  violates  either  of  these  laws  we 
know  is  impossible,  not  merely  in  thought,  but  in 
reality.  We  cannot  allow  that  a  thing  can  differ 
from  itself,  or  that  it  can  both  be  and  not  be,  or 
that  it  can  neither  be  nor  not  be.  AVe  must  regard 
that  as  false  and  unreal  which  these  laws  condemn. 
They  thus  determine  the  sphere  of  impossibility, 
and  that  not  merely  in  thought,  but  in  reality ;  not 
only  logically,  but  metaphysically. 

While,  then,  these  laws  are  no  criterion  of  the 
reality  of  an  object  or  of  the  truth  of  a  proposi- 
tion, they  are  a  strict  and  universal  criterion  of 
non-reality  and  of  falsity.  Thus  they  are  related 
to  existence,  not  positively,  but  negatively.  And 
this  holds  equally  of  all  the  secondary  and  special 
laws  of  logic.  Our  science,  then,  in  its  relation  to 
other  sciences,  is  not  a  positive  criterion  of  truth ; 
it  is  only  _a  Jlfigatiye  criterion,  being  conversant 
with  thoughts,  and  not  with  things ;  with  the  pos- 
sibility, and  not  with  the  reality,  of  existence. 

§  13.  Beside  the  primary  laws  we  place  the 
Postulate  of  Logic  :  L»gic  p»stulates  to  state  £, 
explicitly  all  that  is  implicit  in  a  th»ught. 
As  pure  logic  has  no  concern  at  all  with  the  mat- 
ter of  thought,  so  it  has  none  with  its  language. 
It  deals  not  in  words,  and  must  not  be  bound  by 
them.  Now,  ordinary  speech  is  often  elliptical 
and  rhetorical,  much  of  thought  being  conveyed 


14  INTRODUCTION 

in  hints  and  metaphors.  In  dealing  with  it,  the 
logician  must  be  free  to  strip  off  all  ornament,  to 
supply  all  lacunae,  and  so  exhibit  the  thought 
naked  and  entire.  This  is  sometimes  difficult  to 
do,  thought  being  so  subtile  and  evasive,  and  words 
so  meagre  and  inaccurate.  The  only  limitation  is 
that  the  thought  itself  must  not  be  changed.  Also, 
there  must  be  liberty  to  alter  the  form,  provided, 
likewise,  the  thought  be  not  modified.  JExpressions 
thus  translated  or  transformed  are  equipollent,  and 
the  procedure  is  by  equipollence. 

§  14.  Praxis.  What  point  or  points  of  this  chap- 
ter are  obviously  exemplified,  and  in  what  way 
illustrated,  by  each  of  the  following  propositions  ? 

1.  George  Sand  is  a  woman.     He  is  she. 

2.  Courts  of  justice  are  worse  than  useless. 

3.  That  which  survives  is  the  fittest. 

4.  When  an  irresistible  force  meets  an  insurmountable 

obstacle,  the  result  is  compound  stationary  motion. 
6.  Man  is  the  only  being  that  laughs. 
6.  Will  is  either  free  or  necessitated, 
v.  That  Herod  is  a  fox,  means  that  he  is  cunning. 

8.  Richard  is  himself  again. 

9.  If  death  be  death,  these  have  passed  into  the  past; 
If  death  be  life,  they  live,  though  their  semblance  dies. 

10.  Summum  jus,  summa  injuria. 

11.  A  man  who  never  makes  mistakes,  never  makes  any- 

thing else. 

12.  If  a  man  be  wise,  he  is  cautious,  which  is   to  say, 

Every  wise  man  is  cautious. 
-    13.  His  honor  rooted  in  dishonor  stood. 

And  faith  unfaithful  kept  him  falsely  true. 


PART  I.— CONCEPTION 
I.— THE  NOTION 

§  15.  A  notion  is  either  a  mark  or  a  concept. 
In  _the  forming  of  notions  three  movements  ^f 
thought  may  be  discerned:  abstraction,  general- 
ization, and  conception.     First  of  abstraction. 

When  a  complex  object  impresses  us,  it  is  appre- 
hended as  possessing  qualities.  In  so  far  as  they 
are  dissimilar,  they  cause  in  us  a  feeling  of  differ- 
ence. Now,  if  attention  be  fixed  on  one  quality, 
as  the  color  or  the  weight,  the  other  qualities  be- 
come obscure,  while  this  one  is  drawn  by  attention 
into  vivid  consciousness,  and  so  becomes  the  chief, 
perhaps  the  exclusive,  object  of  cognition.  This 
quality  is  said  to  have  been  abstracted,  or  drawn 
away  from,  the  others,  and  the  process  is  called 
logical  abstraction.  By  it  we  obtain  a  clear  and 
distinct  knowledge  of  the  qualities,  attributes,  char- 
acters, features,  etc.,  that  determine  an  object,  or, 
in  general,  of  its  marks. 

Marks  considered  merely  in  respect  of  their  form 
are  of^eyeral  kinds,  which  may  be  designated_and_ 
exemplified  as  follows : 

1st.  Positive  and  negative ;  as,  rational  is  a 
positive,  and  imperfect  a  negative,  mark  of  man. 


16  CONCEPTION 

2d.  Essential  or  necessary,  and  accidentajjor  non- 
tingent ;  as,  rational  is  an  essential,  and  lea/med  an 
accidental,  mark  of  man. 

3d.  Original  and  derivative ;  as,  rational  is  an 
original,  and  learned  a  derivative,  mark  of  man,  de- 
rived from  his  rationality. 

4th.  Simple  and  complex ;  as,  conscious  is  a  sim- 
ple mark,  it  being  incapable  of  analysis,  and  ani- 
mal a  complex  mark  of  man,  this  being  composed 
of  organized  and  sentient, 

5th.  Common  and  peculiar ;  as,  mortal  is  a  mark 
common  to  man  and  brute,  risible  a  mark  peculiar 
to  man,  found  in  no  other  being.  A  peculiar  mark 
is  called  a  property  when  viewed  apart  from  the 
essence  as  belonging  to  a  certain  class  of  things, 
and  to  no  other ;  as  risible  is  a  property  of  man, 
¥nd  a  property  of  the  circle  is  that  the  chord  of  60° 
is  equal  to  the  radius.  A  peculiar  mark  is  called  a 
particular  jaark  when  it  is  found  onlyJg_asingle 
individual ;  as  the  mark  set  upon  Cain. 

A  mark  is  very  often  thought  of  as  though  it 
were  itself  a  substantial  thing.  Instead  of  being 
referred  to  its  original  substance,  it  is  completely 
severed  therefrom  by  thought,  and  established  in 
an  independent  but  fictitious  existence.  Marks  so 
treated  are  called  abstractions,  and  are  expressed 
by  abstract  terms,  very  many  ending  in  -ness.  E.  g., 
hhie  is  a  concrete  mark  of  the  sky,  of  the  ocean,  of 
sapphire,  etc. ;  but  blueness  is  thought  of  as  some- 
thing independent  of  these  things  and  having  a 
real  existence  apart,  which  is  a  mere  fiction  of 


THE   NOTION  17 

thought.  Likewise,  Aristides  is  just,  but  we  extol 
justice  apart  from  any  person.  Here  the  mark 
jiist  is  thought  as  concrete  in  the  man,  inhering 
in  him ;  but  justice  is  thought  as  abstract  and  hav- 
ing independent  being.  So  human  is  a  concrete, 
huma/nity  an  abstract  term.  A  concrete  term  is 
the  name  of  an  inhering  mark ;  an  abstract  term 
is  the  name  of  a  mark  viewed  as  an  independent 
and  substantial  thing. 

§  16.  In  observing  several  objects,  we  note  that 
they  differ  in  some  respects,  or  produce  dissimilar 
impressions;  perhaps  we  also  note  that  they  are 
alike  in  some  respects,  or  produce  similar  impres- 
sions. The  repetition  of  an  impression  is  precisely 
what  excites  atte^ition,  and  determines  the  direc- 
tion of  reflection.  Thus  consciousness  is  concen- 
trated naturally  on  those  objects  which  partially 
agree,  and  then  on  those  respects  or  marks  in  which 
they  agree.  For  example,  we  observe  a  horse,  an 
ox,  a  goat,  a  dog,  and  we  note  that  each  has  four 
feet,  in  which  respect  they  agree.  When  marks 
are  entirely  similar  the  impressions  they  make  on 
us  are  indistinguishable.  But  what  we  cannot  dis- 
tinguish is  to  us  virtually  the  same.  Accordingly, 
we  consider  them  to  be  the  same,  though  really  in 
different  objects.  This  act,  to  think  the  similar 
the  same,  _  is^  to  generalize — is  generalization.  We 
think  that  each  of  the  animals  named  above  has 
the  same  mark,  four-footed.  A  plurality  is  reduced 
to  unity,  and  the  generality  of  the  mark  consists 
2 


18  CONCEPTION 

in  this,  that  it  may  be  said  of  any  of  the  objects. 
Generalization  is  a  fiction  of  thought,  but  without 
it  our  limited  powers  would  be  unable  to  grasp  the 
multiplicity  of  objects  about  us. 

Generalization  is  classification,  another  aspect  of 
the  same  operation.  By  thinking  a  mark  as  com- 
mon to  several  individuals,  we  thereby  group  them ; 
we  constitute  a  class.  Thus,  the  animals  named 
belong  to  the  group  or  class  quadruped. 

Now,  in  considering  this  group  of  quadrupeds 
we  note  that  the  ox  and  goat  each  have  horns ;  so 
we  generalize  and  call  them  homed  quadrupeds. 
The  horse  and  dog  have  no  horns ;  so  we  general- 
ize and  make  a  group  of  non-horned  quadrupeds. 
This  is  specialization,  correlative  to  generalization. 
We  have  marked  off  two  species,  the  homed  and 
the  non-horned^  the  A  and  the  non-A^  subordinate 
to  the  genus  or  universe  quadruped^  which  is  their 
sura.  It  is  obvious  that  specialization  is  the  inveree 
of^eneralization,  inyolyes  it,  and  Hkewise  is  clas- 
sification. 

§  17.  A  third  movement jofjthought  is  concep- 
tion, its  product  acoT^f^f^pt.  To  ooncpiv<j is  to  grasp 
together.  When^  a  number^  of  marks  have  been 
abstracted,  they^may^  be  collected  by. thought  into 
one  notion,  and  so  constitute _a  concept.  A  cqn- 
cept,  then,  is  a  union  of  marks,  or  a  bundle  of 
marks,  thought  as  belonging  to  some  thin^. 

Each  object  has  an  indefinite  plurality  of  marks. 
Many  of  them  may  be  known  to  us,  but  a  mental 


THE   NOTION  19 

representation  of  an  object  becomes  confused  if  we 
attempt  to  grasp  into  one  or  comprehend  more 
than  a  very  few  of  them.  We  therefore  make  a 
selection  of  some  distinctive  and  some  essential 
marks  to  form  our  concept,  and  must  be  content 
with  this  partial  and  inadequate  representation. 
For  example,  I  take  the  marks  Athenian,  inquisi- 
tive, virtuous,  moralist,  fam^ws,  Tumrtyr,  these  and 
perhaps  others,  to  constitute  my  notion  of  Socrates. 
I  may  know  much  more  about  him,  but  practically 
this,  or  some  such  limited  group  of  marks,  com- 
prises all  I  use  in  representing  him.  On  the  sup- 
position that  these  marks  have  not  been  general- 
ized, the  concept  is  complex,  but  not  general.  Yet 
a  notion  thus  formed  of  an  individual  is  potentially 
general,  potentially  a  class  notion.  There  might 
be  several  persons  having  all  the  marks  here  at- 
tributed to  Socrates.  We  must  then  add  a  partic- 
ular mark,  as,  Plato's  teacher,  to  the  notion  and 
thus  secure  its  individuality. 

When  a  concept  is  constituted  of  marks  that 
have  been  generalized,  that  is,  of  common  marks, 
the  notion  is  then  both  complex  and  general.  It  is 
a  class  notion,  comprising  the  objects  to  which  the 
marks  are  common.  For  example,  I  take  the  fol- 
lowing marks,  which  I  have  abstracted  and  general- 
ized, each  of  which  I  have  thought  as  common  to 
a  large  number  of  objects :  self-  luminous,  Iright, 
sparJding,  celestial,  very  distami,  relatively  fixed,  etc. ; 
and,  making  a  unity  of  this  plurality,  I  form  the 
concept  sta/r.    This  complex  notion  is  applicable  to 


20  CONCEPTION 

each  of  a  host  of  distinct  objects,  in  which  fact  its 
generality  consists ;  and  the  word  star^  which  stands 
for  this  bundle  of  marks,  is  the  common  name  of 
many  individual  things.  A  general  concept,  then, 
is  a  combination  or  reduction  to  unity  in  thought 
ofsimilar  marks  of  objects,  thereby  constitujinga 
class. 

§  18.  The  three  momenta  we  have  described  are 
not  separate  and  successive  in  thinking,  but  are  so 
distinguished  and  stated  to  enable  us  to  compre- 
hend what  is  actually  an  indivisible  operation.  It 
is  merely  a  logical  analysis  of  an  activity  whose 
movements  co-operate  and  coexist. 

Moreover,  a  mark  and  concept  are  commutable. 
Every  mark  is  potentially  a  concept,  and  every  con- 
cept potentially  a  mark.  Thus  :  Man  is  animal^  or 
Man  is  an  animal.  Here  animal  is  first  a  mark, 
then  a  concept.  The  distinction  consists  in  the  use 
made  of  the  notion.  If  used  connotatively,  the  no- 
tion is  a  mark ;  if  used  denotatively,  the  notion  is  a 
concept.  Man  is  animal  means  that  man  has  the 
attributes  connoted  by  the  mark  a/nimaZ.  Man  is 
am,  animal  means  that  man  is  one  of  the  kind  of 
things  denoted  by  the  concept  animal. 

§  19.  A  notion  would  immediately  fall  back  into 
the  infinitude  and  confusion  from  which  it  has  been 
called  out,  were  there  not  some  especial  means  to 
render  it  permanent.  This  is  accomplished  by  a 
word.    The  notion  is  fixed  and  ratified  by  a  verbal 


THE   NOTION  21 

sign,  by  means  of  which  it  can  easily  be  recalled. 
Language,  even  in  mere  denominatioii,  is  a  register 
of  thought. 

The  name  of  a  general  notion  is  a  common  noun. 
Every  common  noun  consists  of  one  or  more  at- 
tributes belonging  to  each  of  several  objects.  It 
stands  for  a  product  of  thought,  and  is  a  factitious 
unit  useful  in  further  thought.  A  mark  is  expressed 
by  an  adjective  noun,  a  concept  by  a  substantive 
noun,  and  an  abstract  noun  is  the  name  of  a  mark 
thought  as  a  thing.  Let  it  be  observed  that  many 
notions,  both  marks  and  concepts,  are  registered  in 
phrases  instead  of  single  words;  as,  for  instance, 
there  is  no  single  word  to  express  the  notion  of 
morally  weak,  or  of  a  rainy  day.  Also,  a  verb  is 
the  naming  of  an  action  or  passion  or  mere  being. 

A  common  naun  is  often  used  to  designate  an 
individual  object  or  group  by  prefixing  a  limiting 
word ;  as,  a  seng,  this  world,  those  hooks,  my  house, 
the  king,  your  friends,  these  troubles,  etc.  Such 
naming  designates  the  object,^though_ indi vidual- 
ized,  as,  belonging  to  a  class.  The  terms  are  con- 
notative ;  they  imply  marks,  and  attribute  these 
marks  to  the  object  or  group  they  indicate. 

A  proper  noun,  strictly  taken,  is  non-connotative. 
It  denotes  an  individual,  but  in  itself  does  not  im- 
ply or  indicate  any  qualities  or  marks  of  the  indi- 
vidual. It  is  an  unmeaning  sign  which  we  connect 
in  our  minds  with  an  object,  so  that  when  it  meets 
our  eyes  or  ears  it  recalls  to  mind  the  thing.  This 
is  true  of  names  strictly  proper.   But  a  name  stand- 


22  CONCEPTION 

ing  for  a  notion  of  an  individual  is  evidently  a  com- 
plement of  marks,  as  the  example  in  §  17  of  the 
notion  Socrates.  Moreover,  names  of  individuals 
are  often  so  contrived  that  they  indicate  their  class; 
thus,  names  of  persons  generally  distinguish  sex, 
also  family  relations;  and  names  of  mere  things 
also  often  have  class  significance,  as  Monticello^ 
Charlottesville^  Fluvanna.  In  such  cases  marks  are 
connoted,  and  there  is  a  distinct  approach  to  the 
common  noun  or  class  name. 

§  20.  Concepts  have  a  twofold  content,  intensive 
andjextensive.  The  intension  is  determinedby  the 
number  of  marks  comj)rehended  by  the  concept. 
E.  g.,  Man  connotes  or  comprehends  the  marks  ex- 
isting^ living,  sentient,  rational.  This  explication  of 
the  connotation  of  a  notion  is  its  determination  or 
definition.  The^uantity  of  extension,  isjdetermined 
by  the  number  of  specific  concepts  or^  of  objects 
contained  under  the  concept).  E.g.,  J/aw  denotes  or 
contains  under  it  the  species  logician,  chemist,  tirtist, 
mechanic,  etc.  This  explication  of  the  denotation 
of  a  notion  is  its  specification  or  division. 

If  the  marks  constituting  the  content  of  a  con- 
cept be  few,  it  may  extend  to  many  things ;  if  the 
marks  be  many  and  distinctive,  the  concept  extends 
to  few  things.  Thus  the  concept  hird  has  few 
marks,  as  animal,  hijped,  feathered,  winged,  etc., 
but  is  applicable  to,  or  contains  under  it,  a  great 
variety  and  number  of  things;  now  the  concept 
swan  has  at  least  one  more  mark,  web-footed^  and 


THE   NOTION  23 

the  variety  and  number  of  things  denoted  is  less. 
Hence  the  Law  :  The  greater  the  intension^ 
the  smaller  the  extension,  and  vice  versa; 
or,  these  contents  are  in  inverse  ratio. 

We  think  a  predicate  either  as  a  mark  or  as  a 
class ;  as,  Facts  are  stubborn^  or,  Facts  are  stuhhorn 
things.  The  one  is  thinking  in  intension,  the  other 
in  extension.  True,  these  involve  each  other,  are 
essential  correlatives,  and  are  readily  convertible ; 
we  do  not  think  the  one  without,  at  the  same  time, 
thinking  the  other.  But  usually  one  mode  is  in 
vivid  consciousness,  while  the  other  is  obscure,  and 
either  phase  of  thinking  may  become  habitual,  one 
person  more  attentively  considering  the  qualities 
of  a  thing,  another  regarding  it  as  a  member  of  a 
class. 

§  21.  Progress  in  knowledge  consists  chiefly  in 
rendering  concepts  clear  and  distinct.  Jllonception  £_ 
is  first  ©bscure  and  then  clear.  We  think  a  concept 
clearly  when  it  is  distinguished  as  a  whole  from 
other  wholes,  ^his  is  accomplished  by  negative 
judgments  distinguishing  or  setling^apart  other 
concepts  from  this  one,  especially  those  which  lie 
nearest  to  it,  or  by  remarking  a  specific  difference. 
E.g.,  We  have  a  clear  knowledge  of  the  faces  of  our 
friends,  since  we  readily  know  one  from  another. 
So  we  have  a  clear  notion  of  horse  when  Ave  know 
that  it  is  not  ox^  nor  a^s,  nor  mnle.  So,  also,  our 
knowledge  of  justice  is  clear  when  we  know  that  it 
is  not  truth^  nor  henevolence^  nor  wisdom,  nor  power. 


24  CONCEPTION 

Our  notion  of  perfurae  is  cleared  by  noting  its 
specific  difference ;  it  is  something  that  can  be 
smelled. 

Clear_conce£tion  is^Jirst  confused,  then  distinct. 
We  think  a  concept  distinctly  when,  viewing  it  as 
a  plurality,  we  distinguish  the  marks  or  the  objects 
that  constitute  it.  Distinctness  is  attained  by  af- 
firma.tive  judgments.  Analytic  abstraction  pre- 
cedes, and  is  followed  by  a  synthesis  wherein  the 
mark  is  affirmed  of  the  thing.  Or  the  notion  is  ap- 
plied to  its  various  objects,  and  in  this  becomes 
known  by  what  is  contained  under  it.  E.  g.,  An 
artist  knows  distinctly  the  features  he  has  deline- 
ated. An  artisan  knows  the  virtues  of  his  tools,  and 
also  their  various  kinds.  Itjs  naturaPand  logical, 
when  one  undertakes  to  explain  any  obscure  matter, 
to  begin  by  clearing  it,  especially  of  thase  tilings 
tEaTlie  nearest  to  it — that  is,  which  most  nearly  re- 
semble it — showing  that^it  is  not  these,  and  then 
j^oceeding  to  render  it  distinct  by_pointing_out 
what  it  is  Tn  Itself,  or  to  what  it  applies. 

Distinctness,  then,  has  two  modes:  one  which 
notes  the  marks  which  a  notion  connotes,  distinct- 
ness in  intension  ;  the  other  which  netes  the  ob- 
jects it  denotes,  distinctness  in  extension.  Inten- 
sive distinctness  is  attained  by  logical  definition, 
which  enumerates  marks.  Extensive  distinctness 
is  attained  by  logical  division,  which  discovers 
kinds.  A  primitive  notion,  such  as  identity,  can  be 
cognized  only  per  se.  However  clear  it  may  be, 
it  has  no  distinctness,  either  intensive  or  extensive. 


THE   NOTION  25 

§  22.  Praxis.  Write  answers  to  the  following 
questions,  and  make  reference  to  the  section  and 
paragraph  illustrated : 

1.  Name  the  kinds  of  these  marks  of  an  apple:  red 
(e.  g.,  positive,  accidental,  original,  simple),  round,  juicy  with 
cider,  innocuous,  grown  on  this  stem,  worth  five  cents.  Also 
of  preachers  as  they  ought  to  be,  these :  unselfish,  called 
to  this  ministry,  hortatory,  devoted,  well  informed,  spiritu- 
ally minded,  widely  sympathetic,  all  things  to  all  men. 

2.  Name  which-  of  the  foll®wing  terms  are  concrete  and 
which  abstract:  troth,  truthful,  trueness,  true,  truthful- 
ness, wisdom,  wise,  foolish,  folly,  consciousness,  individu- 
ality, gratitude,  homely,  straight,  a  straight  line,  a  circle, 
a  fault,  mercy,  improved  health,  a  healing  balm, 

3.  Wliat  marks  constitute  your  notion  of  Caesar  ?  What 
denotation  has  the  word?  What  concept  is  formed  of: 
small,  hard,  transparent,  brilliant,  elementary,  precious, 
ornamental  ? 

4.  What  mark  is  common  to :  chair,  sofa,  stool,  bench  ? 
What  general  marks  characterize  the  concepts :  teacher, 
preacher,  doctor,  lawyer,  author  ?  What  specific  mark  dis- 
tinguishes teacher,  preacher,  and  author  from  the  others  ? 

6.  Change  the  quality  noble  into  a  concept.  Distin- 
guish the  notion  book  from  this  book.  Is  Kaiser  a  com- 
mon or  proper  name  ?  Has  the  name  Mary  Jones  John- 
son any  meaning  ? 

6.  Give  the  intension  of  the  concepts:  war-ship,  hexa- 
gon, wisdom  (see  James  iii.  17).  Give  the  extension  of 
the  concepts:  vessel,  triangle,  wisdom  (cf.  James  iii.  15). 

7.  Clear  the  concept  piano-forte  ;  then  render  it  distinct 
intensively,  then  extensively.  Make  a  note  on  the  logical 
procedure  in  1  Cor.  xiii. 


II.— RELATIONS 

§  23.  The  relations  which  notions  bear  to  each 
other  need  fuller  explication.  As  preliminary,  a 
very  important  and  thorough  -  going  distinction 
should  be  made  between  two  wholes  in  or  under 
which  the  mind  thinks  its  objects.  They  are  these : 
1st.  The  Qualitative  or  Logical  Whole.  This  is 
ipif  two  sorts : 

{a)  The  intensive  whole,  whose  parts  are  marks. 

(J)  The  extensive  whole,  whose  parts  are  kinds. 
2d.  The  Quantitative  or  Mathematical  Whole ; 
of  two  sorts : 

{a)  The  integral  whole. 

(5)  The  collective  whole. 
These  primary  forms  of  the  notion,  the  qualitative 
and  the  quantitative,  should  be  carefully  observed. 
Heretofore  we  have  considered  solely  the  former 
(§15  sq.).  It  is  entirely  subjective,  a  creation  of 
thought,  and  its  parts  are  separable  only  by  ab- 
straction.  It  is  ge.neral,^ndjts  parts  are  general. 

The  latter  is  not  so  entirely  subjective,  since^it  is 
often  determined  by,  and  so  corresponds  to,. aajob- 
jective  reality,  and  its  parts  are  separable  pnly_bj 
dissection;^  It  is  individual,  and  its  ^arts  are  ind^ 
vidual. 


BELATIONS  27 

The  importance  of  this  distinction  is  seen  in  that, 
although  both  forms  intermingle  in  our  thoughts, 
reasoning  in  one  of  these  wholes  is  regulated  by 
principles  differing  from  those  regulating  it  in 
the  other.  Radical  defects  in  the  common  logical 
theory,  as  well  as  many  superfluities,  are  due  to  a 
neglect  of  the  distinction.  The  oversight  occurs, 
probably,  because  nearly  every  notion  is  capable 
of  being  viewed  in  either  whole,  either  as  a  quali- 
tative common  notion  or  as  a  quantitative  total ; 
and  its  transference  from  one  of  these  aspects  or 
forms  of  thought  to  the  other  is  often  very  facile, 
taking  place  almost  unconsciously.  This  does  not 
make  it  a  matter  of  indifference,  but  is  a  reasoo*'*^ 
why  we  should  the  more  carefully  note  this  subtile 
play  of  thought,  so  as  not  to  be  misled  by  it  into 
illogical  confusion. 

We  shall  proceed  to  discuss  the  qualitative  or 
logical  whole  minutely  and  at  length.  In  the  next 
section,  however,  and  occasionally,  we  shall  make 
mention  of  the  quantitative  whole  so  far  as  is  need- 
ful to  distinguish  it  clearly,  and  to  recognize  it  when 
it  occurs  in  qualitative  propositions  Its  full  dis- 
cussion is  postponed  to  §  125  sq. 

§  24.  The  quantitative  or  mathematical  whole, 
then,  is  individual ;  that  is,  not  capable  of  division 
into  kinds.  An  individual  is  indi/visum  in  se,  et  di- 
visum  ah  omni  alio.__  Formally,  it  is  a  unit  viewed 
as  a  quantity,  and  consisting  of  portions  severable 
in  thought.     These  are  evolved  by  cutting  asunder 


28  CONCEPTION 

the  whole;  that  is,  by  partition  or  section,  which 
must  be  clearly  distinguished  from  logical  division. 
Such  parts  are  neither  marks  nor  kinds,  but  merely 
new  individuals. 

First,  the  integral  whole  is  that  in  which  the 
whole  is  before  the  parts.  The  sections  may  be 
hohiogeneous,  as  a  hexagon  severed  into  similar  tri- 
angles ;  or  heterogeneous,  as  a  human  hody,  con- 
sisting of  head,  trunk,  and  limbs.  Anatomy  is  a  sci- 
ence of  partition  or  dissection.  The  general  notion 
sword  logically  divides  into  the  kinds  sabre,  rapier, 
etc. ;  but  each  sword  consists  of  and  is  separated 
by  thought  into  the  sections  hilt,  blade,  etc. 

Second,  the  collective  whole  is  that  in  which  the 
parts  are  before  the  whole.  Such  are  the  notions 
of  an  army,  ^forest,  a  town,  formed  by  repetition 
of  the  notions  of  a  soldier,  a  tree,  a  house.  We 
should_not  confuse  the  general  notion  of  army, 
which  is^  class  notion  capable  Qf_division_iiLto 
kinds,  with  the  particular  notion  of  some  one  army, 
which  is  an  individual,  and  can  only  be  parted  into 
sections,  as  regiments.  These  are  not  kinds  of  a/rmy, 
but  each  is  a  new  individual. 

Quantitative  notions  occur  frequently  as  the  sub- 
ject of  qualitative  propositions,  but  never  as  the 
predicate. 

§  25.  In  the  qualitatiye^jntensive  whole,  notions 
areji^ted  as  congruent,  incongruent,  and-conflic- 
tive.  Congruent  notions  are  such  asmay  coexist  in 
thought.     All  identical  notions  are  congruent,  as 


RELATIONS  29 

cbchromatic  and  colorless.  Also  many  that  arc  not 
identical,  as  learned  and  virtuous^  heautij  and  riches. 
Incongruent  notions  are  such  as  cannot  unito  in  tlio 
saine_obJ6ct,  as  a  musical  rose,  a  hlue  Monday.  Ar- 
istotle asks,  Is  hapjpiness  praiseworthy  f  There  is 
no  answer,  for  the  question  has  no  meaning.  It  is 
an  incongruous  jumble.  Conflictive  notions  deny 
(^ach  other,  as  virtue  and  vice,  heauty  and  deformity, 
rich  and  ^c>6>r.     They  are  in  opposition. 

Of  congruent  notions  one  involves  or  compre- 
hends others  when  these  are  marks  connoted  by  it. 
Thus  the  notion  Socrates  involves  hoih.  famous  and 
Atheniam..  These  are  co-ordinate,  being  both  imme- 
diately comprehended.  But  Athenian  further  in- 
volves Greek ;  and  Greek,  European  /  and  Europe- 
an, human.  It  is  evident  that  these  are  not  equally 
proximate  and  immediate  in  Socrates,  and  that  they 
are  in  the  relation  of  part  to  whole.  They  2iYQ  par- 
tes intra  partes ;  yet  each  permeates  and  informs 
the  whole.  So  chalk  is  both  white  and  hrittle,  and 
these  marks  coexist  throughout. 

In  the  qualitative,  extensive  whole,  notions  have 
the  relations  of  coextension,  subordination,  co-ordi- 
nation, and  intersection.  These  may  be  figured 
thus: 


Globe 
Coextension  [O.s )  l-^pfTerT 


Animal 
Subordination 


30 


Co-ordination 

m&) 

Weapon 
I  Sword    1  Spear 

Intersection 

(-f) 

Protestants 
1         Irish 

The  circular  notation  needs  no  explanation.  In 
the  linear  notation  a  horizontal  line  expresses  the 
extension  of  a  notion  ;  the  comparative  length  and 
the  relative  position  of  two  such  lines,  the  relation 
of  two  notions.  The  vertical  line  indicates  affirma- 
tion ;  its  absence,  negation  (§§  86,  87). 


§  26.  Two  notions  are  coextensive  when  they 
have  the  same  denotation.  They  may  be  symbol- 
ized by  two  coincident  circles.  The  following  are 
coextensive :  globe  and  sphere,  triangle  and  trilater- 
al, endogens  and  monocotyledons,  double-refracting 
and  polarizing  crystals,  to  conquer  one^ s passions  and 
to  become  master  of  one's  self  Either  of  two  such 
notions  may  be  thought  of  as  contained  under  the 
other.  Coextension  should__be^distin^uished  from 
eguality  which  expresses  quantitative  relation. 

§  27.  One  notion  or  concept  is  subordinate  to  or 
contained  under  another  when  it  comprehends  the 
same  and  more  marks  an^  extends  to  fewer  objects 
(§20).  "TTis  aTspecIes.  Thus,  ma^  is  a  species  of 
animal,  and  sword  is  a  species  of  weapon.  The 
former  is  subordinate  to  the  latter;  it  connotes 


RELATIONS  31 

more  marks^  but  it  denotes  fewer  objects.  The 
superior  concept,  since  more  objects  are  contained 
under  it,  is  the  more  general  notion.  It  is  a  genus. 
Thus  animal  is  the  genus  of  man  ;  weapon,  of  sword. 
Both  genera  and  species  are  classes,  and  the  ar- 
rangement of  things  according  to  genera  and 
species  is  classification  (§  16). 

It  is  manifest  that  these  forms  of  thought  are 
merely  relative.  A  genus  may  be  contained  under 
some  higher  concept,  and  then  relatively  to  this 
higher  genus  it  is  a- species.  /Thus  weapon  is  a 
species  of  the  genus  mMnxuwut.  A  species  may 
contain  under  it  some  lower  concept,  and  then  rel- 
atively to  this  lower  species  it  is  a  genus.  Thus 
sioord  is  a  genus  of  the  species  sabre.  A  notion 
that  is  thus  alternately  a  genus  relatively  to  lower, 
narrower  concepts,  and  a  species  relatively  to  some 
higher,  broader  concept,  is  called  a  subalternate  or 
subaltern  genus.  It  is  characterized  as  a  genus 
that  may  become  a  species. 

A  genus  is  a  universal  notion  or  a  universe  (§  9), 
since  it  turns  the  many  parts  into  the  unity  of  a 
whole.  This  is  the  logical  meaning  of  universe,  ad 
unum  versus,  giving  e'plurihus  unum.  It  is  often 
called,  by  way  of  eminence,  a  logical  whole.  A 
species  is  a  special  or  specific  notion,  and  since  it  is 
but  a  part  of  the  generic  whole  it  is  a  particw\a,v 
notion.  The  species  as  parts  make  up  the  genus 
as  a  whole  (§  10).  These  are  partes  extra  partes, 
since  they  are  distinct  groups  of  objects;  as  dia- 
monds and  rubies  are  species  oi  jewels.     Hence  we 


32  CONCEPTION 

can  symbolize  by  circles  or  lines  the  relations  of 
concepts  in  extension,  but  not  of  those  in  intension. 

§  28.  Praxis.  "Write  answers  to  the  following 
questions,  referring  to  the  section  and  paragraph 
descriptive  of  the  point  in  question : 

1.  In  which  whole  do  we  think  :  the  world,  the  planets, 
disorder,  a  flash,  thunder,  war,  King  Henry  ?  Transfer 
each  to  the  other  whole. 

2.  What  kind  of  quantity  is :  a  constellation,  a  tree,  a 
mob,  Mt.  Blanc,  a  sphere,  a  dollar,  the  ocean,  this  book  ? 

3.  "What  is  the  intensive  relation  of :  money  and  mem- 
ory, simple  and  complex,  magnanimity  and  stature,  an 
aching  void,  saint  and  sinner,  sweet  and  sour,  ray  dwelling- 
house  is  built  of  brick  burned  with  fire  ? 

4.  What  is  the  relation  in  extension  of :  brute  and  dog, 
heat  and  motion,  seeing  and  perceiving,  frankness  and 
candor,  lyric  and  hymn,  hymn  and  sacred  lyric,  gun  and 
cannon,  bimana  and  mankind?  Write  the  circular  and 
linear  notation  in  connection  with  each  pair. 

6.  Considering  chair,  monarchy,  and  poetry,  each  as  a 
subaltern  genus,  what  genus  is  each  contained  under,  and 
what  species  is  contained  under  each  ? 

6.  What  partes  extra  partes  constitute  the  entire  logical 
universe :  animal,  triangle,  doctrine,  lake,  history,  logical 
whole  ? 


m.— DIVISION 

§  29.  The  relation  of  co-ordination  is  evolved  by 
logical  division  (§  25).  It  has  already  been  seen 
that  by  specification  we  form  subordinate  groups 
whose  members  are  co-ordinate.  Since  pure  logic 
considers  only  the  form,  each  genus  or  universal 
whole  can  contain  only  two  species,  marked  with 
A  and  non-A.  For  A  being  a  generic  difference, 
that  is,  a  mark  not  found  in  the  genus  or  divisum, 
but  found  in  some  of  its  members,  we  know  a  pri- 
ori, witheut  any  consideration  of  the  matter  of 
thought,  that  the  members  are  exclusive  of  each 
other  and  exhaustive  of  the  divisum.  This  is  di- 
vision by  dichotomy,  and  the  members  are  contra- 
dictories (§  9).  For  example :  languages  are  Aryan 
and  non-Aryan,  O/nimals  are  vertebrate  and  inver- 
tebrate, the  ancients  were  Greeks  and 
barbarians.  The  process  viewed  inten- 
sively, as  thinking  marks  in,  is  determi- 
nation; viewed  extensively^  as  distin- 
guishing^ species,  it  is  specification^  (§  20).  In  rela- 
tion to  each  other,  the  two  species  are  co-ordinate, 
being  of  equal  rank  in  respect  of  the  divisum ;  but 
we  remark  that  either  may  be  of  indefinitely  great- 
er extent  or  breadth  than  the  other. 
3 


34  CONCEPTION 

§  30.  The  negative  member  of  a  dichotomy  is 
characterized  by  the  absence  of  the  mark  A^  or,  in 
other  words,  by  the  negative  mark  nan- A.  Hence 
arise  negative,  privative,  or  infinitated  concepts. 
Often  their  sphere  is  very  wide,  denoting  almost 
everything,  and  connoting  very  little,  almost  noth- 
ing positive.  E.  g.,  unhounded^  inert,  wpathy,  blind, 
free,  absolute,  infinite.  In  many  cases  a  notion, 
originally  a  mere  negative  of  its  co-ordinate,  has 
received  a  positive  mark,  so  that  either  or  both  of 
the  members  of  the  dichotomy  may  be  regarded  as 
positive.  E.  g.,  happy  and  unhappy,  true  and  un- 
true or  false,  honor  and  dishonor,  man  and  brute, 
town  and  country,  i.  e.,  the  contrary.  Notions  es- 
sentially negative,  but  whose  name  does  not  indi- 
cate this  character,  are  often  opposed  by  terms  neg- 
ative in  form,  yet  positive  in  fact.  Thus  temperate, 
verbally  positive,  is  a  negative  notion,  opposed  to 
the  positive  intemperate,  which  is  negative  in  form. 
So  also  ease  or  health  and  disease,  pure  and  impure. 

Notions  strictly  correlative  originate  in  dichoto- 
my. The  two  always  coexist  in  thought.  We 
may  be  thinking  more  of  one  member  of  the 
couple  than  of  the  other,  but  if  either  exists  the 
other  coexists  with  it  in  consciousness,  if  either  be 
expressed  the  other  is  implied.  For  example :  pa- 
rent and  child,  ruler  and  subject,  cause  and  effect, 
heavy  and  light,  up  and  down,  rich  and  poor,  genus 
and  species,  positive  and  negative.  This  last  pair  is 
the  origin  and  generalization  of  aU  correlatives. 
One  of  the  two  is  usually  more  or  less  negative,  and 


DIVISION  35 

in  case  a  separate  name  has  not  been  adopted  for 
each,  the  noi^^ative  correlative  to  any  positive  notion 
may  be  expressed  by  the  prefix  dis-y  un-^  or  m-,  or 
the  suffix  -ee  or  -less.  For  example  :  conscious  and 
unconscious,  correct  and  incorrect,  truster  and  trus- 
tee, godly  and  godless,  A  and  non-A. 

§  31.  In  divisions  not  purely  logical,  but  having 
respect  to  the  matter,  it  often  occurs  that  we  have 
those  that  are  more  than  dichotoraous ;  we  may 
have  a  trichotomy  or  a  polytoray.  E.  g,,  doctrines 
are  helpful,  harmless,  hurtful.  This  arises  from 
two  causes.  Either  it  is  an  abbreviation,  whereby 
several  species,  in  turn  subordinate,  are  condensed 
into  one  co-ordinate  statement ;  as,  angles  are  7'ight 
(and  non-right,  which  are)  acute  and  obtuse.  Or  it 
arises  from  the  lack  of  a  sharp  definition  of  our 
concepts.  There  is  often  between  two  opposite 
thoughts  a  notion  or  notions  which  it  is  impossible 
to  identify  surely  with  either,  and  so  constituting 
a  tertium  quid,  a  third  species,  which  it  is  needful 
to  insert  in  order  to  exhaust  the  divisum.  Thus 
we  have  age  distributed  as  young,  middle-age,  old; 
so  also,  riches,  competence,  want  /  also,  white,  gray, 
Mack.  For  many  of  these  intermediate  species  we 
have  no  name ;  as  between  sick  and  well,  strong  and 
weak,  long  and  short,  wise  s^nd  foolish. 

We  have  remarked  that  in  a  strictly  logical  dis- 
tribution the  members,  A  and  non-A,  are  contra- 
dictories ;  no  member  of  that  universe  cdn  be  both, 
or  can  be  neither  (§  9  and  §  29).     In  a  trichotomy 


36  CONCEPTION 

or  a  polytomy  the  members  are  disparate  notions. 
Thus,  hrooh,  cr^e^mjerare^  disparates,  contained 
under  the  genus  streams.  Any  two  of  such  a  di- 
vision, as  hrook  and  river,  are  logical  contraries ;  a 
thing  of  this  genus  cannot  be  both,  but  may, be 
neither ;  it  may  be  the  tertium  quid. 

Finally,  a  polytomous  division  admits  of  one, 
and  only  one,  strictly  privative  or  negative  notion. 
Thus,  some  men  lend,  some  horrow,  some  do  hoth, 
some  do  neither.  The  intermediate  ground,  well 
named  the  undefined  or  indifferent  part,  often 
takes  this  negative  character ;  as,  men  are  very  mi- 
dustrious,  positively  lazy,  and  neither  the  one  nor 
the  other. 

§  32.  A  thoughtful  consideration  of  the  preced 
ing  discussion,  together  with  the  illustrations,  will 
discover  that  each  division  is  made  with  reference 
to  some  general  character  or  mark  of  the  genus  di- 
vided. In  dividing  animals,  for  example,  into  ra- 
tional and  irrational,  reference  is  made  to  their  in- 
telligence. Also  in  distributing  loolcs  into  folios^ 
quartos,  etc.,  the  reference  is  to  their  size.  This 
generic  mark,  or  character  of  the  di  visum,  which 
reappears  in  a  distinct,  modified  form  as  at  once  a 
generic  and  a  specific  difference,  is  called  thej)rin- 
ciple  or  ground  of  thejdivision,  the  fundameni/um 
dimsionis. 

A  strict  procedure,  then,  would  be  this :  "We  as- 
semble representative  instances  of  the  objects  de- 
noted by  the  divisum,  and  having  fixed  upon  a  gen- 


DIVISION 


37 


eric  mark  as  the  principle  of  division,  we  select  a 
mark  immediately  involving  this  principle  to  serve 
as  a  specific  difference.  Then  we  divide  the  deno- 
tation by  affirming  the  specific  difference  of  the 
class  which  it  determines,  and  denying  it  of  all 
other  contained  objects.  In  subsequent  divisions 
we  do  likewise,  involving  in  each  new  specific 
difference  the  one  immediately  preceding,  and,  of 
course,  the  original  principle. 

A  nominal  or  artificial  division  is  one  made  for  i^ 
some  transient  purpose,  or  to  attain  a  practical 
end ;  or  one  tentative  and  precursory  to  a  real  di- 
vision ;  or  one  popularly  accepted  and  useful,  such 
as  the  numbers  that  may  be  observed  on  every 
page,  and  in  every  few  minutes  of  conversation. 
A  real  or  scientific  division  is  one  proposing  to  di- 
vide notions  and  things  according  to  their  true  and 
essential  nature,  in  order  to  attain  correct  objective 
knowledge  of  things  as  they  are.  Such  division 
develops  natural  kinds,  and  is  to  be  looked  for  in 
the  more  refined  sciences.  The  Linnaean  artificial 
divisions  of  flora  were  precursory  and  tentative; 
those  of  Jussieu's  natural  system  are  real  and' 
more  rigidly  scientific. 

§  33.  The  old  saying,  Divide  et  impera,  may  be  "^ 
freely  translated  by  Classify  and  conquer.  In 
treating  any  matter,  so  great  is  the  practical  value 
of  correct  logical  division,  the  root  of  classification, 
that  we  now  gather  up  the  foregoing  principles  in 
the  following  Rules  : 


38  CONCEPTION 

1st.  The  ground  of  a  division  should  be 
an  essential  or  at  least  an  important  mark 
of  the  di visum.  The  ground  or  principle  select- 
ed should  be  essential,  if  we  would  attain  to  real, 
scientific  knowledge.  It  should  be  important,  im- 
porting other  attributes,  if  we  would  evolve  an  ex- 
tended and  valuable  series.  The  purpose  of  an 
artificial  division  fixes  its  ground.  In  civil  affairs 
it  would  be  absurd  to  divide  men  into  horsemeri 
si^nd  footmen,  but  in  military  affairs  this  is  impor- 
tant. In  grammar,  words  are  distributed  accord- 
ing to  syntactical  relations ;  in  a  dictionary,  alpha- 
betically. Medical  botany  and  the  florist's  manual 
distribute  plants  differently,  and  both  differ  from 
Jussieu.  "We  sort  our  hooJcs  by  size  to  fit  our 
shelves,  by  subjects  for  handy  reference,  by  binding 
for  show. 

2d.  The  members  should,  as  parts,  equal 
the  whole  divisum.  'No  one  should  exhaust  the 
genus;  as  in  sciences  are  deductive  and  inductive, 
whereas  all  sciences  use  deduction.  Together  they 
should  exhaust  it ;  which  is  the  case  in  angles  are 
right  and  oblique,  but  not  in  governments  are  mo7ir 
archies  and  democracies,  for  there  are  other  kinds. 

3d.  The  species  should  emerge  immedi- 
ately from  the  genus.  The  genus  should  be 
proximate ;  as  in  plants  are  powering  and  jlower- 
less.  Thought  should  not  overlook  and  overleap 
subaltern  genera,  and  proceed  directly  to  remote 
species ;  as  in  plants  are  annual,  biennial,  and  per- 
ennial.   This  rule  relates  chiefly  to  strict  scientific 


DIVISION  39 

classification.  In  other  matter  the  hiatus  is  quite 
usual  and  useful ;  as  in  plants  are  noxious  and  imr 
noxious. 

4th.  Only  one  principle  should  be  used  in 
determining  a  series.  The  use  of  different 
grounds  of  division  in  a  series  gives  rise  to  the  log- 
ical fault  called  cross  division.  Thus:  vertebrates 
are  quadrumana,  hima/na^  quadrupeds,  and  hijpeds. 
Here  two  grounds  of  division  are  used,  first  nuTn- 
ler  of  hands,  then  of  feet.  We  have,  consequently, 
a  cross  division,  himana  and  hipeds  are  communi- 
cant species,  they  overlap  in  mam.. 

Such  a  series  is  tested  by  dichotomy.  Any  cor- 
rect trichotomy  or  polytomy  may  be  reduced  to  a 
dichotomy  by  taking  any  one  member  as  positive, 
and  including  the  rest  under  its  negative.  Thus  : 
Substances  are  a/nimal,  and  vegetable,  and  mineral. 
Tested:  S  are  a  and  no7i-a  {=v-^m)',  ov  v  and 
nonyv  {■=a-\-7n)',  or  m  and  non-m  (=«  +  ■?;).  This 
test  applied  to  the  following  polytomy  will  dem- 
onstrate it  to  be  logically  vicious :  Religious  sects 
are  catholic,  calvinist,  episcopal,  and  dissenting. 

§  34.  Praxis.  Write  answers  to  the  following 
questions  and  requisitions : 

1.  Which  of  these  are  positive,  and  which  are  negative 
notions,  and  what  are  the  opposites  of  each  :  dry,  simple, 
stranger,  protestant,  atheist,  shadow,  calm,  disorder,  sober, 
living,  restless,  iniquity,  silence,  unclean  ? 

2.  What  notions  are  correlate  to  :  teacher,  north,  above, 
useful,  right,  committee,  beggar,  payer,  pastor  ? 


40  CONCEPTION 

3.  What  tertium  quid  lies  between :  day  and  night,  hot 
and  cold,  love  and  hate,  far  and  near,  joy  and  sorrow  ? 
What  is  the  logical  relation  of  these  notions? 

4.  What  is  the  fundamentum  divisionis  of  the  follow- 
ing: conduct  is  interested  and  disinterested,  animals  are 
herbivorous  and  carnivorous,  sounds  are  agreeable  and  dis- 
agreeable ? 

5.  Assign  a  principle  upon  which :  houses,  fruits,  his- 
torical periods,  and  tariff  laws  may  each  be  dichotomized. 

6.  Criticise  the  following  examples,  that  is,  state  whether 
they  are  logical  divisions  or  quantitative  partitions  (§  23). 
If  divisions,  state  whether  they  are  correct  or  not ;  and  if 
not,  what  rule  or  rules  are  violated : 

(a.)  The  human  hand  consists  of  palm  and  fingers  ;  it  is 
flexible  and  expert ;  and  known  as  right  and  left. 

(b.)  Propositions  are  aflirmative,  hypothetical,  and  negative. 

(c.)  Logic  is  deductive  and  inductive.  The  former  treats  of 
conception,  deduction,  and  fallacy, 

(d.)  Imaginative  writers  are  poets,  dramatists,  and  novelists. 

(e.)  The  seasons  of  the  year  are  spring,  summer,  autumn, 
and  winter. 

(f.)  Men  are  rational  and  fanatic. 

(g.)  Religions  are  Christian  and  Antichristian. 

(h.)  Men  are  Americans,  Europeans,  blacks,  and  pagans. 

Y.  Make  several  divisions  of  citizens,  stating  the  ground 
of  each,  into  the  species :  laity,  aliens,  peers,  natives,  clergy, 
commons. 

8.  Divide  mankind  on  the  principle  of :  age,  sex,  fam- 
ily relations,  color,  riches,  education,  occupation,  and  dis- 
position. 


IV.— DEFINITION 

§  35.  The  relation  of  intersection  is  discovered  ^ 
in  definition  (§  25).  Now,  as  division  has  reference 
primarily  to  extension,  so  definition  refers  prima- 
rily to  intension.  Our  thought,  having  been  cleared 
(§  21),  is  by  these  rendered  distinct ;  the  external 
or  extensive  distinctness  being  secured  by  division, 
the  internal  or  intensive  distinctness  by  definition. 

A  definition  is  the  explication^_gf  the  essential 
and  original  marks  of  a^concept,  the  definitum. 
Thus :  Mam,  is  defined  as  rational^  sentient^ivin^, 
existing.  It  is  evident,  however,  that  this  mode  of 
statement  is  awkward,  and  in  many  cases  impracti- 
cable. Observing,  then,  that  the  notion  animal  in- 
volves successively  sentient,  living,  existing,  we  sub- 
stitute for  them  that  mark,  and  define  summarily  : 
Man  is  rational  and  ammial.  The  mark  rational^ 
not  included  in  the  summation,  is  distinctive,  since 
of  all  the  notions  that  we  here  connote,  it  belongs 
to  man  alone.  A  logical  definition,  then,  consists 
of  two,  and  only  two,  essential  and  original  marks, 
one_being  commonj^the  other  djstinctive. 

§  36.  From  the  foregoing  principles  are  derived 
three  corollaries,  as  follows : 


42  CONCEPTION 

1st.  „Simple  notions,  having  no  plurality  of  marks, 
are  incapable  of  definition.  The  notion  of  a  heing^ 
since  it  has  only  the  one  mark  existing,  and  no  dif- 
ferential or  distinctive  character,  is  indefinable,  is 
an  indefinite  notion. 

2d.  An  individual  cannot  be  defined.  Practi- 
cally, we  cannot  enumerate  its  essential  and  orig- 
inal marks,  or  sum  up  all  those  it  has  in  common 
with  any  other  notion  or  thing.  It  can  only  be 
described. 

3d.  Since  the  definitum,  or  notion  defined,  con- 
tains implicitly  the  marks  which  its  definition  con- 
tains explicitly,  they  are  reciprocating  or  converti- 
ble concepts.  Thus :  A  triangle  is  a  polygon  of  three 
sides  /  and,  reciprocally,  A  polygon  of  three  sides  is 
a  triangle.  Hence  either  may  replace  the  other. 
Thus :  Every  rectilineal  figure  may  he  cut  into  tri- 
a/ngles  ;  or,  by  replacement,  Every  rectilineal  figure 
may  he  cut  into  polygons  of  three  sides. 

§  37.  Though  definition  relates  primarily  to  in- 
tension, it  is  readily  and  usually  viewed  in  relation 
to  the  extension  of  a  concept.  Concepts  in  exten- 
sion often  intersect;  that  is,  two  concepts  often 
have  a  common  part,  and  each  a  part  not  com- 
mon (§  25).  Thus  there  are  Irish  Protesftants,  also 
there  are  Irish  not  Protestants,  and  Protestamis  not 
Irish.  The  common  part  is  a  species  which  is  con- 
tained under  either  of  the  total  concepts  as  a  ge- 
nus. In  other  words,  whenever  a  certain  group  of 
things  may  be  referred  as  a  species  to  either  of  two 


DEFINITION  43 

genera,  these  genera  intersect,  the  group  being  a 
common  part. 

Now,jthe  two  portions  of  a  definition  may  each 
be  viewed  as  a  concept  in  extension.  If  so,  they 
will  be  seen  to  intersect,  and  the  definitum  to  be 
the  common  part.  Thus,  the  notion 
rational  being  intersects  the  notion  /^  ?S^\ 
animal  /  man^  being  both,  is  the  com-  \  \J  J 
mon  part.  Formally,  the  definitum 
may  be  referred  to  either  concept  as  a  genus ;  log- 
ically, neither  has  preference ;  but  whichever  be 
chosen,  the  other  serves  to  mark  off  or  limit  the 
definitum. 

Thus  we  get  the  usual  form  of  the  logical  defi-  c 
nitiqn.  Itconsists  of  the  genus  proximate  to  the 
definitum,  together  with  its  specific  difference.  The 
proximate  genus  is  that  class  under  which  the  no- 
tion defined  is  immediately  contained ;  as  animal 
is  the  proximate  genus  to  the  concept  man.  The 
specific  difference  is  that  which  thoroughly  distin- 
guishes the  notion  defined  from  all  other  species  of 
that  genus ;  as  rational  is  the  specific  difference 
distinguishing  man  from  all  other  species  contained 
under  animal,  as  beasts,  birds,  fishes,  etc.  Thus  we 
have,  Man  is  a  rational  animal.  Also,  Logic  is  the 
science  (=prox.  gen.)  of  the  necessary  formes  of 
thought  (=spc.  dif.).  Such  is  the  formal  definition 
per  genus  et  differentiam. 

§  38.  For  the  sake  of  clear  treatment,  it  should  L 
at  once  be  remarked  that  any  predicate  consisting 


44  CONCEPTION 

of  two  or  more  qualitative  notions  may  be  viewed 
as  a  genus  with  a  difference.  Thus :  Negroes  are 
docile  (=dif.)  creatures  (=gen,).  Here  the  genus 
is  not  proximate,  and  the  difference  is  neither  es- 
sential nor  thorough-going.  So,  also :  Faith  is  the 
assura/nce  of  things  hoped  foi\  etc.  No  clear  think- 
ei  will  mistake  these  for  definitions. 

A  description  recites  constituent  parts  of  a  thing, 
especially  such  as  are  of  interest  and  importance  and 
at  the  same  time  distinctive,  the  selection  being  gov- 
erned by  a  purpose.    It  may  approximate  definition. 

An  accidental  mark  or  a  property  (§  15)  may  be 
used  to  set  a  notion  clearly  apart ;  as,  Man  is  a 
featherless  hiped ;  or.  Body  only  is  mobile.  This  is 
definite,  but  not  definition. 

A  predicate  generalizing  the  conditions,  or  the 
consequences,  or  explicating,  not  the  connotation, 
but  the  denotation,  is  merely  a  quasi  -  definition. 
Thus:  Motion  is  the  product  of  force  and  tinie  • 
Malaria  is  feverous  air  /  Mind  is  that  which  knows 
and  feels,  desires  and  wills.  This  last  is  evidently 
a  division  rather  than  a  definition.  Such  forms  are 
often  spoken  of  as  definitions  a  posteriori  /  but  a 
logical  definition  is  strictly  a  priori. 

§  39._A.real_defiiiitiQiLjexplicates  the  essence  of 
a  real  object  or  class,  in  the  forms  of  it&__pi:0xi- 
mate  genus  and  specific  difference.  It  is  a  priori 
and  analytic.  It  has  the  character  of  a  proposi- 
tion affirming  both  the  reality  and  the  nature  of 
the  thing  defined.     Such  are  the  verified  defini- 


DEFINITION  45 

tions  of  science;  as,  Table-salt  is  sodium  chloride; 
Attention  is  consciousness  concentrated  on  an  object. 
Definitions  of  abstract  notions  derived  from  reali- 
ties must  also  be  accounted  real ;  as,  A  circle  is  a 
plane  figure  whose  outline  is  everywhere  equally 
distant  from  some  point. 

A  nominal  definition  is  of  the  name  of  an  object 
or  class  having  only  an  ideal  or  hypothetical  ex- 
istence; as,  a  centaur;  open  polar  seas.  In  prac- 
tice the  distinction  between  the  nominal  and  the 
real  cannot  always  be  clearly  applied ;  for  nominal 
definitions,  being  often  tentative  and  preliminary, 
may  become  real. 

A  genetic  or  causal  definition  is  concerned  with 
the  rise  or  production  of  a  thing,  considering  it, 
not  as  being,  but  as  becoming.  Thus :  A  came  is  a 
solid  generated  by  the  revolution  of  an  angle  about 
one  of  its  sides.  The  notion  defi^ned,  not  being 
given  but  made,  this  definition  is  a  priori  and 
synthetic. 

§  40.  The  original  essence  being  known,  help  in 
making  or  criticising  a  definition  is  given  by  the    ^ 
following  practical  Kules  : 

A  logically  correct  definition  should _be  : 

1st.  Positive.  The  definition  is  always  to  be 

aflBrmed    of    tlie    definitum. Negative    statements 

serve  to  render  the  notion  clear,  and_are_important 
precursors  to  definition,  but  they  do  not  render  a 
notion  distinct  (§  21).  "When  the  subject  is  a  posi- 
tive notion,  which  is  most  frequently  tlie  case,  the 


46  CONCEFnON 

definition  predicated  of  it  should  consist  of  j)08i_tize 
notions.  A  definition  should  tell  what  a  thing  is, 
not  what  it  lacks,  or  what  it  is  not ;  as,  A  line  is 
length  without  breadth ,'  and.  Pleasure  is  the  feeling 
opposed  to  pain.  When,  however,  a  notion  is  essen- 
tially negative,  as  shadow.,  freedom,  gentile,  want, 
then  its  definition  should  be  n^ative;  as,  Inverte- 
hrates  are  animals  destitute  of  an  internal  skeleton. 

2d.  Adequate.  If  the  genus  be  not  proximate, 
the  definition  is  too  wide ;  as,  Man  is  a  rational 
being.  If  the  difference  be  not  thorough-going — 
that  is,  not  common  to  all  members  of  the  class — 
the  definition  is  too  narrow  ;  as,  Man  is  a  praying 
animal.  A  convenient  test  of  adequacy  is  con- 
vertibility (§  36). 

3d.  Not  tautological.  It  should  not  contain 
the  name  of  the  thing  defined,  nor  a  synonym,  nor 
a  correlative  term,  for  this  is  to  define  a  thing  by 
itself.  Thus :  A  lawmaker  is  one  who  makes  law  ; 
Life  is  the  sum  of  the  vital  functions  /  A  cause  is 
that  which  produces  an  effect.  Reciprocal  defini- 
tions are  not  allowed ;  as,  A  board  is  a  thin  plank, 
and  a  plank  is  a  thick  board.  This  is  a  sort  of 
logical  seesaw.  It  is  called  defining  in  a  circle, 
and  by  the  Greeks  diallelon  (through  each  other). 
There  is  a  similar  vice  in  reasoning  called  by  the 
same  name  (§  146). 

4th.  Precise.  It  should  contain  nothing  merely 
accidental ;  as,  The  potato  is  the  food  of  the  Irish. 
This  difference  is  an  accident  (§  15).  It  should  con- 
tain nothing  superfluous ;  as,  A  triangle  is  a  figure 


DEFINITION  47 

ha/ving  three  sides  and  three  angles.  Here  is  super- 
fluity. Names  of  forms  should  not  be  included 
with  names  of  things ;  as,  The  mir  is  a  species  of 
dog,  etc.  Here  species  is  superfluous.  Derivatives 
being  implied  by  their  originals  should  be  excluded 
as  superfluous ;  as,  Honest  dealing  is  rendering  to 
every  one  his  own  property.  Here  the  notion  of 
own^  derived  from,  property,  is  superfluous. 

5th.  perspicuous.  It  should  be  intelligible,  lit- 
eral, and  brief.  A  definition  proposes  to  make  a 
notion  distinct ;  hence  the  use  of  notions  more  ob- 
scure than  the  one  to  be  defined  violates  perspi- 
cuity ;  as.  The  soul  is  the  Ji/rst  enteUchy  of  an 
organized  hody  possessing  life  potentially.  Again, 
all  figurative  notions  should  be  excluded,  for 
tropes  do  not  indicate  what  a  thing  is,  but  only 
something  similar ;  as.  Omnipresence  is  a  circle  of 
which  the  centre  is  everywhere  a/nd  the  circumfer- 
ence nowhere.  Many  expressions,  however,  origi- 
nally metaphorical  have  become  literal,  and  may 
properly  be  used  in  defining.  Finally,  brevity  is 
certainly  a  merit,  but  extreme  brevity  may  be  less 
perspicuous  than  needless  prolixity. 

§  41.  Praxis.  Analyze  into  genus  and  differ- 
ence, classify  by  giving  the  kind,  and  criticise  by 
applying  the  principles  and  rules,  the  following 
questionable  definitions! 

1.  Philosophy  is  the  science  of  principles. 

2.  Gratitude  is  the  memory  of  the  heart. 

3.  Motion  is  the  change  of  place  of  body. 


48  CONCEPTION 

4,  Motion  is  the  act  of  potential  being  up  to  the  meas- 
ure of  its  potentiality. 

6.  Motion  is  an  accidental  property  of  body  that  effects 
a  changing  of  its  place. 

6.  Mad  call  I  it ;  for,  to  define  true  madness, 
What  is't  but  to  be  nothing  else  but  mad  ? 

V.  Green  is  a  color  compounded  of  blue  and  yellow. 

8.  Silence  is  the  entire  absence  of  sound  or  noise. 

9.  Mind  is  unextended  substance. 

10.  Mind  is  conscious  substance. 

11.  Health  is  the  condition  of  a  living  body  free  from 

disease  or  pain. 

12.  A  spheroid  is  a  solid  formed  by  the  revolution  of  an 

ellipse  about  its  diameter. 

13.  Opium  is  a  vegetable  product  which  causes  sleep. 

14.  A  dragon  is  a  serpent  breathing  flame. 

16.  A  synopsis  is  a  conspectus  of  the  chief  points. 
16.  Animal  is  the  genus  denoting  men  and  brutes. 
IV.  Psychology  is  the  science  of  the  phenomena  of  mind. 

18.  Logic  is  the  light-house  of  the  understanding. 

19.  Dirt  is  matter  in  the  wrong  place. 

20.  Pleasure  is  the  reflex  of  normal  activity. 

21.  An  atom  is  an  ultimate  particle  of  matter  incapable 

of  division. 

22.  A  circle  is  a  curved  line  returning  upon  itself,  all  the 

points  of  which  are  equidistant  from  a  given  point 
within  called  the  centre. 

23.  A  point  is  position  without  parts  or  magnitude. 

24.  Time  is  a  measured  portion  of  indefinite  duration. 

25.  Laws  are  the  expressed  will  of  a  ruler;  and  a  nilei 

is  one  whose  will  is  expressed  in  laws. 


v.— SYSTEM 

§  42.  As  preliminary  to  an  examination  of  logi- 
cal system,  we  will  present  and  remark  upon  the 
foUowinof  scheme : 


-1  C  Existing Minerals,  Plants,  Brutes,  Men.  "1  ^ 

S  J  Existing,  living Plants,  Brutes,  Men.  }  « 

2-  j  Existing,  living,  sentient Brutes,  Men.  (  S 

P  t  Existing,  living,  sentient,  rational Men.  J  w 

The  most  obvious  point  here  illustrated  is  the  law 
that  as  intension  increases,  extension  diminishes, 
and  vice  versa ;  that  the  maximum  of  either  is  the 
minimum  of  the  other ;  that  the  two  are  in  inverse 
ratio  (§  20). 

In  ascending  the  series,  we  think  marks  out  and 
think  things  in.  This,  on  the  intensive  side,  is  ab- 
straction (§  15) ;  on  the  extensive  side,  it  is  general- 
ization or  generification  (§  16). 

In  descending  the  series,  we  think  marks  in  and 
think  things  out  in  the  same  mental  act.  This,  on 
the  intensive  side,  is  determination ;  on  the  exten- 
sive side,  it  is  specialization  or  specification. 

§  43.  The  same  matter  in  a  modified  form,  with 
some    additions,   is   presented    in    the    following 
scheme : 
4 


50 


CONCEPTION 


Second  Intentions. 
Concepts  of  Forms. 


First  Intentiona 

Concepts  of 

Things. 


Intension  or  Depth. 
Maries  connoted. 


I   ExteDBion  or 

Breadth. 
Things  denoted. 


Sunamum  Genus 
Species  or  Sub-genus 
Species  or  Sub-genus 
Iniima  Species 


Being  or  Thing 
Organism 
Animal 
Man 


Existing 
Ex.,  living 
Ex.,  Iv.,  sentient 
Ex.,  Iv.,  sn.,  rational 


All  Things 
All  Organisms 
All  Animals 
All  Men 


Individual 


Aristotle 


-h- 


Ditto,  Father  of  Logicl  One  Being 


Here  is  represented  a  complete  logical  system 
founded  on  the  relation  of  genus  and  species.  It 
should  be  thoughtfully  examined  by  the  student  of 
logic,  in  all  its  details,  some  of  which  we  now  pro- 
ceed to  discuss. 


§  44,  It  is  evident  that  thought,  rising  from  indi- 
viduals to  classes,  and  by  successive  generalizations 
forming  wider  and  wider  classes  or  genera,  at  each 
step  diminishing  the  marks  connoted,  must  at  last 
reach  a  notion  of  widest  generality,  connoting  but 
one  mark  and  denoting  all  things,  above  which,  of 
course,  it  cannot  rise.  This_highestL widest  notion 
is  the  Summum,  Genus,  and  is  characterized  as  the 
genus  that  cannot~15ecome  a  spmes!  ITls  repre- 
sented  in  the  foregoing  scheme  by  Being  or  Thing, 
which  are  synonymous,  comprehending  only  the 
mark  Existing,  and  containing  under  it  All  Tilings. 

It  is  possible  to  analyze  metaphysically  and 
logically  the  notion  heing  or  thing  into  its  constit- 
uent notions  matter  and  farm  (§  4).  It  is  therefore 
referable  to  the  stiU  higher  genus  matter,  and  so 
is  definable  thus :  A  thing  is  mutter  hamng  fcyrm,. 
In  this  view,  mutter,  taken  in  its  widest,  metaphys- 


SYSTEM  61 

ical  sense,  is  the  true  summum  gentts.  We  shall, 
however,  for  convenience,  continue  to  speak  of  be- 
in^  or  thing  as  the  actual  summum  genus,  simple, 
indefinable,  and  ultimate. 

In  departments  of  science,  it  is  not  usual  to  make 
reference  to  this  common  genus.  For  each,  its  own 
subject  is  regarded  as  summum  genus,  that  notion 
which  is  characterized  by  the  mark  selected  as  its 
yundamentum,  dwisionis  {%  32).  Thus,  in  botany, 
plant  is  the  highest  genus  considered ;  in  zoology, 
animal;  in  political  economy,  wealth;  in  logic, 
thought  form.  They  leave  to  metaphysics  or  ontol- 
ogy, the  science  of  being,  the  exploration  of  the 
still  higher,  more  rarefied  region.  Similarly,  in 
more  commonplace  matters,  some  subaltern  genus 
(§  27)  is  usually  assumed  as  ultimate. 

But  the  frequent  use  of  the  word  thing  shows 
what  constant  mental  reference  is  had  to  the  actual 
summum  genus.  Indeed,  whenever  we  do  not 
know  the  proximate  or  approximate  genus  of  an 
object,  or  do  not  care  to  be  exact,  we  mount  up  on 
eagle  wing  and  call  it  a  thing ;  thus :  A  comet  is  a 
curious  thing.  Likewise  it  is  used  as  an  index  of 
mere  existence;  as,  Evil  is  an  unavoidahle  thing. 
Again,  if  we  wish  to  consider  an  object  relative  to 
some  one  mark  exclusively,  we  call  it  a  thing ;  as, 
Wins  is  a  hurtful  thing,  because,  etc.;  or  if  we 
wish  to  emphasize  some  mark;  as.  Cruelty  is  a 
hateful  thing. 

§  45.  On  the  other  hand,  when  thought  descends    L 


52  OONOEPTION 

the  scale,  and  by  successive  specifications  forming 
narrower  and  narrower  classes  or  species,  at  each 
step  adding  marks  and  so  rejecting  things,  it  must 
at  last  reach  a  class  of  narrowest  generality,  con- 
noting a  maximum  plurality  of  common  marks, 
and  denoting  a  minimum  plurality  of  things,  belo\y 
which,  of  course,  it  cannot  descend.  This  Jo  west, 
narrowest^lass  is  the  Infima  Species,  and  is_char- 
acterized  as  the  species  that  cannot  become  a  genus. 
It  is  represented  in  the  foregoing  scheme  byTMan-, 
comprehending  many  common  marks,  and  contain- 
ing under  it  only  individual  human  beings. 

The  early  logicians  consider  the  infima  species 
as  fixed  by  nature,  and  expressed  in  the  terms 
mmij  horse,  etc.  Such  classes  as  negro,  harh,  etc., 
they  do  not  admit  to  be  species,  but  merely  acci- 
dental varieties.  But  the  whole  question  of  natural 
kinds  belongs  exclusively  to  the  naturalist,  and 
with  it  the  logician  has  nothing  whatever  to  do. 
In  logical  theory,  which  disregards  matter  (§4), 
system  is  restricted  only  by  the  primary  laws  of 
thought.  Hence  division  into  logical  kinds  pro- 
ceeds until  no  mark  common  to  even  two  individ- 
uals remains  to  serve  as  a  specific  difference.  The 
species  that  comprehends  all  the  common  marks  is 
theoretically  the  infimia  species,  for  that  alone  can- 
not become  a  genus  by  further  division. 

§  46,  It  is  important  to  observe,  clearly  and  dis- 
tinctly, what  relation  individuals  bear  to  the  logi- 
cal system.    This  system  consists  of  classes  only, 


SYSTEM  53 

and  hence  an  individual  is  not  a  member  of  it. 
For  an  individual  is  not  a  kind,  is  not  a  logical  part 
(§  24) ;  that  is,  it  cannot  be  evolved  by  division.  It 
is  evident  ex  vi  termini  that  the  infima  species  has 
no  subordinate.  It  follows  that  the  objects  of  which 
a  class  is  formed  cannot  in  strictness  be  spoken  of 
as  contained  under  the  class,  though  this  expression 
is  used.  More  properly  the  class  is  said  to  denote, 
not  only  its  species,  but  also  the  objects  or  things 
it  comprises. 

But  individual  objects  are  the  basis  of  all  classi- 
fication (§§  16,  32).  Now,  it  is  not  necessary  in 
generalizing  that  we  should  begin  with  the  infima 
species  and  thence  build  up  the  scale.  It  is  com- 
petent to  begin  with  any  wide  class  and  evolve 
the  system  downward  and  upward.  This  indicates 
that  any  and  every  genus  denotes,  not  only  its  sub- 
ordinate classes,  but  also  all  the  individual  things 
of  which  it  can  be  predicated. 

An  individual,  as  the  word  itself  points  out,  is 
logically  indivisible  (§  24).  But  this  is  a  mark  also 
of  infima  species.  What,  then,  distinguishes  the  one 
from  the  other?  Principally  that  the  latter  is  a 
class,  the  former  not.  Thus,  while  the  latter  con- 
sists of  common  marks  only,  the  former  possesses 
also  at  least  one  particular  mark,  represented  in 
the  scheme  by  Father  of  Logic.  This  particular 
mark  determines  only  a  numerical,  not  a  specific, 
difference ;  and  therefore  the  individual  cannot  be 
defined,  yet  may  be  described  (§  38).  Such  is  the 
logical  individual  (§  17).    The  real,  actual  Individ- 


54  CONCEPTION 

ual  possesses  also  a  distinct  existence  in  space  or 
time.  It  is  discriminated  by  perception,  external 
or  internal.     It  has  many  numerical  differences. 

§  47.  It  is  apparent  that  division  and  definition 
are  correlative  forms  (§  30).  As  division  is  con- 
cerned with  the  extension  or  breadth  of  a  concept, 
so  definition  is  concerned  with  its  intension  or 
depth.  By  the  one  a  notion  is  rendered  externally 
or  extensively  distinct;  by  the  other  it  is  rendered 
internally  or  intensively  distinct  (§  21).  A  division 
explicates  or  evolves  subordinate  concepts ;  a  defi- 
nition explicates  or  evolves  marks.  The  one  devel- 
ops the  sphere,  the  other  the  comprehension.  The 
one  analyzes  the  denotation,  the  other  the  conno- 
tation. To  each  of  the  forms  herein  named  is  op- 
posed a  correlative. 

In  a  systemized  series  of  concepts,  division  looks 
down,  definition  up,  the  scale.  When  a  specific 
subject  is  to  be  treated,  we  first  define  it ;  we  give 
its  proximate  genus,  the  one  next  above,  which  in- 
volves all  the  marks  of  the  preceding  genera,  in- 
cluding the  highest ;  we  also  give  its  specific  differ- 
ence, which  sets  it  apart  from  co-ordinate  notions. 
Then  we  proceed  downward,  dividing  and  subdi- 
viding, until  we  reach  and  include  the  lowest 
species.  This  exhausts  the  scale,  and  the  treat- 
ment is  logically  complete.  Of  course  it  is  not 
necessary  that  this  order  should  be  rigidly  ob- 
served. In  the  progress  of  a  treatise,  definition 
may  often  replace  division,  and  one  or  the  other 


SYSTEM  55 

will  preponderate  according  to  the  point  in  the 
scale  at  which  a  beginning  is  made,  or  according  to 
the  inclination  of  the  thinker  or  the  nature  of  his 
subject. 

But  since  division  and  definition  are  convertible 
correlatives,  a  system  may  be  expressed  entirely 
in  either,  they  being,  mutatis  mutandis^  the  same 
form.  We  may  begin  with  the  summuin  genus, 
and,  descending,  exhaust  the  scale  by  a  series  of 
divisions.  Or  we  may  begin  with  the  imfiina  spe- 
cies, and,  ascending,  exhaust  the  scale  by  a  series 
of  definitions.  Any  specific  concept  being  de- 
fined, it  is  requisite  to  define  the  proximate  genus 
to  which  it  is  referred,  and  again  the  proximate 
genus  to  which  this  is  referred,  and  so  on  until  the 
summuin  genus  is  reached. 

Certain  sciences,  as  botany  and  zoology,  are 
sometimes  called  classificatory  sciences,  because 
they  exhibit  their  matter  mostly  in  the  form  of 
divisions.  But  all  sciences  are  classificatory,  and 
those  referred  to  should  rather  be  called  dividing 
sciences.  On  the  other  hand,  chemistry  is  emi- 
nently a  defining  science.  Having  named  the  ele- 
ments, it  uses  few  other  names,  a  compound  being 
designated  generally  by  its  definition  only ;  as, 
potassium,  iodide,  and  nitrate  of  cupric  oxide.  It 
would  be  quite  possible,  however,  to  state  the  rela- 
tions of  chemical  substances  as  genera  and  species. 

Thus  it  is  that  thoughts  are  elaborated  and  ren- 
dered clear  and  distinct  by  being  co-ordinated  and 
subordinated,  by  being  divided  and  defined,  until 


56  CONCEPTION 

they  are  gradually  built  into  systems,  more  or  less 
complete  and  perfect.  Let  it  be  particularly  re- 
marked that  this  is  true  not  merely  of  scientific 
thinking,  but  is  equally  true  of  our  every-day 
thinking,  and  that  about  the  most  trivial  matters 
(§  3).  It  is  thus  that  at  all  times  and  about  all 
things  we  do  think,  and,  governed  by  the  necessary 
laws  of  pure  thought,  it  is  thus  that  we  must  think. 
Every  common  noun  in  a  language  occupies  a  place 
in  some  of  the  countless  hierarchies  of  concepts 
which  the  human  mind  is  forming  or  has  formed. 
It  is  true  that  in  most  minds  there  is  much  con- 
fusion and  disorder  in  the  fabric  of  thought ;  stiU, 
the  greater  part  of  the  humblest  mental  life  is  oc- 
cupied in  generalizing  and  specializing,  in  system- 
atically arranging  and  correcting  the  arrangement 
of  thoughts. 

§  48.  A  series  of  definitions  may  be  expressed 
either  directly,  from  the  lowest  species  upward, 
or  inversely,  as  in  the  examples  given  in  the  next 
section.  A  series  of  divisions  is  generally  best  ex- 
pressed in  the  unnamed  manner  briefly  exemplified 
in  §  23,  in  the  distribution  of  Wholes,  which  should, 
therefore,  be  closely  considered.  The  early  logi- 
cians made  use  of  the  figure  of  a  logical  tree,  arbor 
Porphyriana,  erect,  horizontal,  or  inverted,  from 
which  comes  the  familiar  phrase  "branches  of 
knowledge."  Also  they  used  the  figure  of  a  scale 
or  ladder  {scala,  Kkifia^,  a  staircase).  These  several 
forms  are  illustrated  in  the  next  section. 


SYSTEM  57 

§  49.  Praxis.  The  following  exercises  should  be 
written  with  care,  and  reference  made  to  the  sec- 
tions illustrated : 

1.  Name  a  number  of  individuals  denoted  by  the  wide 
notion  town.  Of  these,  which  are  comprised  by  the  nar- 
rower notion  city?  Of  which  may  metropolis  he  predi- 
cated?      Ok.^JJo..     f^e^'i    fi^^-'jc^   M^-,    /l    k  •  " 

2.  Criticise  the  following  series :  The  TJ.  S.  domain  con- 
sists of  states  and  territories ;  the  states  are  Northern  and 
Southern,  the  Northern  are  Eastern  and  Western,  all  are 
divided  into  counties,  and  these  into  townships,     /^tct^ 

3.  Divide  and  subdivide  officers  of  the  U.  S.  government 
with  reference  to  their  official  functions.     '^-'^  -vf'  (t^^ 

4.  What  is  \\iQ  fundamentum  divisionis  of  the  following 
scala  ?  Reduce  it  to  a  series  of  definitions,  supplying  spe- 
cific differences : 


Chris 

Mankind 

1 

Theists 

1 

Atheists 

1 
Monotheists 

1 

Polytheists 

1 

tians                             Antichristians 

i 

1 
Papists 

1 

Protestants 

5. 

1 
Jesuits 

Change  the 
Viscid 

Non-Jesuits 
following  tree  into 
Gaseous 

a  scale  or  ladder 
non-gaseous 

Liquid                        non 

-liquid 

non- viscid 

Solid 

non-solid 

Matter 


68  CONCEPTION 

^      6.  Describe  the   divisions   exhibited   in  the   following 
horizontal  tree  in  ordinary  language  (of.  §  21) : 

i  Obscure 
(  Conftised  (  Inadequate 

Clear . .  ,.X  i\  Adequate    | 

(  Distinct -J  V  Perfect 

(  j  Intuitive     ) 
I  Symbolic 

V.  Try  to  divide  and  subdivide  triangle  so  as  to  include, 
without  cross  division  (§  33),  the  right-angled,  the  equi- 
angular, the  obtuse-angled,  and  the  isosceles. 

8.  Change  the  following  series  of  definitions,  omitting 
the  specific  differences  and  supplying  negative  members, 
into  a  series  of  divisions,  presenting  a  scala,  as  in  Ex.  4  : 

A  carnivore  is  a  flesh-eating  mammal. 

A  mammal  is  a  vertebrate  suckling  its  young. 

A  vertebrate  is  an  animal  having  an  internal  skeleton. 

An  animal  is  a  sentient  organism. 

An  organism  is  a  living  being. 

9.  Change  the  following  series  of  definitions,  omitting 
and  supplying  as  above,  into  a  series  of  divisions,  present- 
ing a  horizontal  logical  tree,  as  in  Ex.  6 : 

Wealth  is  things  useful  and  agreeable,  acquired  by  labor. 
Capital  is  wealth  destined  to  reproductive  consumption. 
Circulating  capital  is  capital  consumed  in  a  single  use. 
Wages  is  circulating  capital  paid  in  remuneration  of  labor. 

10.  Exhibit  the  following  logical  distribution  of  the  sci- 
ences in  the  manner  exemplified  in  §  23 : 

All  rational  knowledge,  or  philosophy  in  its  widest  sense,  is 
either  a  posteriori  and  empirical,  or  a  prion  and  pure. 
Empirical  knowledge  gives  rise  to  abstract  science,  as 
mathematics ;  and  to  concrete  science,  as  the  inductive 
sciences.  Pure  knowledge,  or  philosophy  in  its  restricted 
sense,  is  either  formal  or  material.  Material  philosophy, 
or  metaphysics,  has  two  branches — a  metaphysic  of  nature 
or  phj'sics,  and  a  metaphysic  of  morals  or  ethics.  The 
chief  sciences  strictly  fgrmal  are  philology  and  logic. 


VL— PREDICATION 

§  50,  To  predicate  is  either  to  affirm  or  deny  one  C- 
notion  of  another.  Since  pure  logic  does  not  at  all 
consider  the  matter  of  propositions,  but  only  their 
form  (§§  4,  12),  it  is  permissible,  according  to  the 
Law  of  Identity,  to  affirm  any  notion  of  any  other, 
provided  they  be  not  contradictories  (§  8).  Thus 
there  is  no  logical  or  formal  fault  in  saying :  The 
inoon  is  made  of  green  cheese  j  or,  The  earth  is  a 
cube ;  or,  Every  man  is  dishonest.  However  false 
to  fact  such  statements  may  be,  they  are  not  logi- 
cally absurd ;  that  is,  in  themselves  essentially  con- 
tradictory. It  is  possible  to  entertain  the  thought. 
But  to  speak  of  a  spherical  cuhe^  or  of  something 
hetter  than  the  best,  or  of  a  complete  vacuum.,  or  of 
our  mutual  friend,  or  of  tempting  providence.,  or  to 
say  that  all  men  are  liars.,  is  logically  absurd,  since 
a  contradiction  is  involved,  and  it  is  not  possible  to 
entertain  a  thought  thus  qualified  (§  9).  In  consid- 
ering predication,  then,  we  are  not  at  all  concerned 
with  the  material  truth  or  falsity  of  what  is  said, 
but  with  the  form  of  the  saying,  which  is  limited 
only  by  self-contradiction. 

§  51.  Predication  is  either  positive  or  negative. 
It  is  the  issue  of  comparison.     Two  notions  com- 


60  CONCEPTION 

pared  are  apprehended  as  similar  or  dissimilar,  and 
the  judgment  pronounces  that  they  agree,  or  that 
they  disagree.  Positive  predication  affirms  or  pos- 
its, by  the  Law  of  Identity,  that  the  subject  and 
predicate  are  in  the  relation  of  part  and  whole,  con- 
tained and  containing.  Negative  predication  de- 
nies or  sublates,  by  the  Law  of  Contradiction,  such 
relation,  excluding  subject  and  predicate  each  from 
the  sphere  or  comprehension  of  the  other.  By  the 
Law  of  Excluded  Middle,  no  third  form  of  predica- 
tion is  possible ;  the  relation  in  question  between 
subject  and  predicate  either  does  or  does  not  exist, 
it  is  yea  or  nay.  The  ground  of  this  division  of  the 
forms  of  predication  is  called  their  Quality ;  that  is, 
judgments,  with  reference  to  their  quality,  are  pos- 
itive and  negative. 

§  52.  When  one  notion  is  predicated  of  another, 
the  existence  of  their  objects  is  neither  posited  nor 
sublated.  To  affirm  that  sea-water  is  salty  does  not 
posit  the  existence  of  sea,  or  of  water,  or  of  salt,  or 
of  the  mark  salty.  This  is  presumed  in  case  of  each, 
the  result  of  prior  thought ;  or  the  affirmation  is 
conditioned  on  their  existence,  thus :  If  there  be 
seorwater,  it  is  salty.  Obviously  to  deny  one  notion 
of  another  does  not  sublate  the  existence  of  their 
objects.  So  far  of  absolute  existence.  Their  rela- 
tive existence  is  predicated,  conditioned  on  their 
absolute  existence ;  that  is  to  say,  if  they  absolutely 
or  really  exist,  a  relation  between  them  is  affirmed 
or  denied  as  existing. 


PREDICATION  61 

But  very  often  there  is  occasion  to  predicate  ab- 
solute existence.  This  is  accomplished  by  existen- 
tial forms  of  speech  or  propositions.  Thus,  I  am 
means  /  exists  lam  existing,  or  /  am  a  being.  The 
predicate  in  such  case  is  the  summum  genus,  or  its 
single  simple  mark.  So,  also,  Chance  is  not;  that  is 
to  say,  there  is  no  such  thing.  Existential  proposi- 
tions frequently  take  an  inverted  form,  the  place  of 
the  transposed  subject  being  occupied  by  a  mean- 
ingless particle ;  as.  It  is  fine  weather ;  There  are 
not  many  wise.  Some  predications  may  be  con- 
strued as  existential  or  otherwise.  Thus  the  latter 
example  may  be  construed  either  as,  Not  mamy  wise 
are.,  or  as,  The  wise  are  not  many. 

§  53.  Negative  forms  call  for  special  remark.  A 
negation  strictly  pure  merely  denies  one  notion  of 
another,  no  more.  If  we  say,  Smohe  is  not  vapor, 
the  thought  is  that  these  two  notions,  though  lia- 
ble to  be  confounded,  are  so  essentially  unlike  that 
they  should  be  set  entirely  apart.  This  is  simply  a 
holding  back  from  error.  In  other  negations  there 
is  a  thought  of  a  genus  which  is  denied  to  the  sub- 
ject ;  as,  Smohe  is  not  a  gas  /  that  is,  the  genus  gas 
does  not  contain  under  it  smoke  as  one  of  its  kinds. 
Thirdly,  there  may  be  a  reference  of  both  notions 
to  a  containing  genus.  Thus  in  Men  are  not  hrutes^ 
the  thought  is  limited  by  the  universe  animal,  un- 
der which  man  and  hrute  are  specific  contradictories 
(§  9).  Lastly,  the  notions  may  be  disparate,  or  con- 
trary, and  as  such  be  denied  of  each  other  (§  31). 


62  CONCEPTION 

A  proposition  whose  predicate  is  a  pure  negative 
is  called  infinite.  If  we  say,  The  soul  is  not  mortal^ 
by  this  denial  we  merely  ward  off  error.  But  if  we 
say,  The  soul  is  non-mortal,  as  to  logical  form  we 
affirm,  and  thereby  place  the  soul  in  the  infinite 
sphere  of  non-mortal  beings.  This  sphere,  obtained 
by  the  subtraction  of  mortals  from  the  infinite 
sphere  of  beings,  though  limited  thereby,  is  stiD 
infinite. 

Very  many  notions  formally  negative  have  never- 
theless a  positive  character  (§  30).  Each  of  these  is 
usually  thought  as  a  finite  mark  or  universe.  Such 
are  the  notions  helpless,  unpleasant,  unwell,  infa- 
mous,  uneven,  im?nortal.  Thus,  if  we  say,  ITie  soul 
is  immortal,  there  is  affirmed  of  it,  besides  the  nega- 
tive notion  of  infinity,  the  positive  one  of  continu- 
ous existence.  This  marks  a  definite  genus,  quite 
distinguishable  from  non-mortal. 

§  54.  Predication  is  either  in  the  intensive  or  m 
the  extensive  whole  (§  23  sq.).  The  distinction  is 
grounded  on  the  relation  of  subject  and  predicate, 
as  reciprocally  whole  and  part. 

In  an  intensive  judgment,  the  subject  is  the  whole 
or  major  term,  the  predicate  is  the  part  or  minor 
term.  Thus,  in  the  attributive  judgment  The  earth 
is  spherical,  the  notion  earth  is  an  intensive  whole 
consisting  of  a  complement  of  marks,  and  the  mark 
spherical  attributed  to  it  enters  into  or  is  recognized 
as  a  part  of  this  whole,  it  being  only  one  mark  out 
of  many  that  characterize  the  notion  earth.     This 


PREDICATION  63 

form  is  conventionally  interpreted,  The  earth  com- 
prehends spherical. 

In  an  extensive  judgment,  the  predicate  is  Jthe 
whole  or  major  term,  the  subject  is  the  part  or 
minor  term.  Thus,  in  the  proposition  The  earth  is 
a  sphere^  the  notion  sphere  is  an  extensive  whole,  a 
genus,  constituted  of  many  kinds  of  things,  as  the 
other  planets,  their  satellites,  the  sun,  the  geomet- 
rical sphere,  globular  fruits,  rain-drops,  etc.  Now, 
the  earth  is  declared  to  be  one  of  the  many  things 
denoted  by  sphere^  to  be  a  part  of  this  whole,  a 
member  of  the  genus.  This  form  is  conventionally 
interpreted,  The  earth  is  contained  under  sphere. 

Consequently,  while  a  qualitative  judgment  may 
have  an  individual  as  its  subject,  it  cannot  have  an 
individual  predicate.  For  the  predicate  in  inten- 
sion is  a  mark,  in  extension  a  genus  (§  20);  an. 
individual  cannot  be  either.  We  may  say.  Great 
is  Diana.,  but  this  is  a  rhetorical  inversion ;  Diana 
is  the  subject,  and  the  predicate  is  great.  We  may 
say.  The  rival  of  Plato  is  Aristotle^  but  this  is  not 
qualitative,  but  a  quantitative  equivalent  proposi- 
tion. 

§  55.  The  ten  categories  or  predicaments  of  Aris- 
totle, about  which  opinions  greatly  differ,  are  as 
follows,  illustrated  by  his  own  examples : 

1.  Substance; — it  is  a  man,  a  horse,  etc. 

2.  Quantity ; — it  is  two  cubits  long,  three,  etc. 

3.  Quality ; — it  is  white,  grammatical,  etc. 

4.  Relation ; — it  is  half  as  large,  greater,  etc. 


64:  CONCEPTION 

5.  Action ; — it  cuts,  burns,  etc. 

6.  Passion ; — it  is  cut,  is  burned,  etc. 

Y.  Place ; — it  is  in  the  Agora,  the  Lyceum,  etc. 

8.  Time ; — it  is  to-day,  was  yesterday,  etc. 

9.  Posture ; — it  is  reclining,  seated,  etc. 

10.  Possession ; — it  is  having  shoes,  armor,  etc. 

These  may  be  interpreted  as  an  exhaustive  series 
of  summa  genera  standing  next  the  true  summum 
genus.  Being ;  metaphysically,  a  classification  of 
the  modes  of  objective  or  real  existence ;  logically, 
a  classification  of  the  most  general  notions  that 
can  be  predicated  of  any  subject.  That  is  to  say, 
anything  whatever  may  be  said  to  be  a  substance, 
a  qucmtity,  or  some  other  one,  at  least,  of  these 
highly  generaUzed  notions.  In  this  view  they  are 
first  intentions  or  names  of  things  (§  4). 

But  it  seems  clear,  both  from  the  title  of  the  list 
and  from  his  examples,  that  Aristotle  intended  to 
name  rather  all  the  possible  forms  underjwliich 
thmgs  may  be  represented  in  thought.  Thus,  if 
we  say  of  anjiihing.  It  is  a  man,  vre  are  thinking 
it  in  the  category  of  substance ;  or,  if  we  say,  It  is 
seated,  we  are  representing  it  in  the  predicament  of 
posture;  and  so  any  judgment  whatever  will  fall 
into  one  or  another  of  these  ten  formal  categories. 
In  this  view  theyare  second  intentions  or^  names 
of  forms  of  thought. 

£,  §  56.  Having  settled  the  category  in  which  a 
predication  places  the  subject,  it  may  be  asked. 
What  kinds  of  predicates  are  then  possible ;  or,  in 


PREDICATION  65 

other  words,  what  are  the  second  intentions  or 
forms  of  its  possible  predicates?  The  answer  is 
Aristotle's  doctrine  of  the  predicables,  as  follows: 
Every  judgment  affirms  or  denies  of  its  subject  one 
or  another  of  these  four  relations : 

1.  Definition;  as,  Man  is  a  ra-  )        .„    ,  ,  ) 

tional  animal f  =  All  of  the  essence     I  Convertible. 

2.  Property ;  as,  Man  is  risible. . . .  =  None  of  the  essence  ; 

3.  Genus;  as,  Man  is  an  animal.  .  =  Part  of  the  essence    ) 

4.  Accident;  as,  Man  is  a  biped. .  r=  None  of  the  essence  j 


It  has  been  proposed  to  substitute  specific  differ- 
ence for  definition,  since  it  already  contains  genus, 
and  to  make  the  number  five  by  adding  species  as 
predicable  of  individuals.  But  the  list  would  not 
be  improved ;  for,  as  Aristotle  himself  remarked, 
both  difference  and  species  are  of  the  nature  of 
genus,  and  interchangeable  with  it  (§§  27,  37). 

§  57.  Praxis.  Write  the  quality  of  each  of  the 
following  propositions,  stating  whether  the  predi- 
cation is  logically  permissible  or  not,  and  why,  and 
noting  existential  forms : 

1.  I  do  not  just  now  remember  anything  I  have  for- 

gotten. 

2.  A  national  debt  is  a  national  blessing. 

3.  There  is  none  that  doeth  good,  no,  not  so  much  as 

one.     Let  there  be  light ;  and  there  was  light. 

4.  A  flying  arrow  is  at  rest. 

6.  Tt  is  impossible  to  love  and  be  wise. 

6.  There  is  a  tide  in  the  affairs  of  men 

Which,  taken  at  the  flood,  leads  on  to  fortune. 

7.  I  think  there  be  six  Richmonds  in  the  field. 

5 


66  CONCEPTION 

8.  Man  is  not  a  beast  for  burdens,  nor  a  reptile  for 

bruising. 

9.  There  is  no  place  like  home. 

10.  Let  us  try  to  amuse  ourselves  by  doing  nothing,  and 

so  making  ourselves  miserable. 

11.  An  idiot  is  irrational.     A  brute  is  non-rational. 

Note  which  is  the  major  term  in  the  following, 
with  the  reason : 

12.  Pearls  are  precious.     Rubies  are  stones. 

13.  Heresy  is  sin.     Solomon  is  wise. 

Predicate  a  categorical  class  of  each  of  these 
subjects : 

14.  Gold.     The  wealth  of  Crcesus.     Antiquity.     Red. 

Parallelism.  A  battle.  New  York.  A  multitude. 
Upright.     A  defeat. 

State  to  what  category  and  to  what  predicable 
each  of  these  judgments  belongs : 

15.  Snow  is  frozen  mist ;  it  falls  lightly  ;  is  very  white ; 

but  is  easily  discolored ;  it  is  colder  than  water ; 
lies  level ;  occurs  only  in  winter ;  but  not  at  the 
equator ;  it  has  minute  crystalline  forms ;  and 
accumulates  in  huge  masses. 


VTL— SIMPLE   PROPOSITIONS 

§  58,  As  a  product  of  thought,  ajudgment  is  the| 
result  of  comparison.     Two  notions  are  compared,! 
and  the  judgment  pronounces  that  they  agree  or  I 
disagree.     In  case  they  disagree,  they  are  set  apart 
by  a  denial.     In  case  they  agree,  they  are  unified 
by  an  affirmation.     To  judge  affirmatively  is  to 
bring  a  notion  into  or  under  another.      One   is 
thought  as  determined  by  the  other;  for  either 
the  latter  is  brought  as  a  mark  into  the  one,  which 
is  thereby  determined,  or  else  the  one  is  brought 
under  the  other  as  a  class,  and  thereby  determined* 
A  judgment  expressed  in  words,  since  it  is  placed 
before  us  for  acceptance,  js^  called  a  proposition. 
What  is  subjectively  a  judgment  is  objectively  at 
proposition.  ' 

The  propositional  forms  with  which  logic  is  im- 
mediately concerned  are  the  conditional  and  the 
categorical.  A  conditional  proposition  states  a 
comparison  so  nearly  complete  that  only  some  pro- 
vision remains  in  question.  The  contingency  is 
expressed  as  a  condition,  thus :  If  air  he  pure,  it  is 
wholesome.  Categorical  propositions  constitute  the 
negative  member  of  the  dichotomy.  A  categorical 
proposition  is  one  wherein  no  contingency  or  condi- 


68  CONCEPTION 

tion  is  expressed.  This  difference  is  obviously  not 
essential ;  but  since  the  conditional  declares  rela- 
tively to  some  provision,  and  the  categorical  names 
none,  the  latter  is  said  to  declare  absolutely.  In 
strictness,  however,  all  propositions,  except  axioms, 
are  conditioned  on  prior  thoughts,  and  on  the  ex- 
istence of  their  objects  (§  52).  The  provision  may  or 
may  not  be  expressed.  While,  therefore,  we  shall 
give  the  conditional  form  special  consideration  in 
a  subsequent  chapter  (§  110  sq.),  we  shall  not  care 
to  exclude  it  meantime  from  view,  though  our  at- 
tention for  the  present  will  be  directed  chiefly  to 
the  categorical  form. 

§  59.  The  categorical  proposition  is  severed  by 
partition  into  three  portions  (§  24).  In  affirmation 
these  are : 

'  1st.  The  notion  of  something  determined,  called 
the  Subject. 

2d.  The  notion  of  something  determining,  eaUed 
the  Predicate. 

3d.  The  part  which  expresses  this  relation,  called 
the  Copula. 

In  the  negative  proposition  there  is  no  determi- 
nation of  one  notion  by  another.  But  in  both  forms 
something  is  spoken  of,  which  is  the  Subject ;  some- 
thing is  said  of  it,  which  is  the  Predicate ;  and  that 
which  says  this  is  the  Copula.  Thus,  Sncw  is  Pure, 
or  S  is  P.  In  early  logic  the  predicate  includes 
the  copula,  and  this  is  stiU  the  usage  of  gramma- 
rians.    But  logicians  now  reckon  the  copula  as  a 


SIMPLE   PROPOSITIONS  69 

distinct  co-ordinate  part.  The  subject  and  pred- 
icate, being  the  extremes  of  the  partition,  are  called 
the  Terms  of  the  proposition.  It  is  not  at  all  req- 
uisite that  a  terra  should  consist  of  a  single  word ; 
each  term  may  be  composed  of  many  words  in  in- 
tricate grammatical  relations.     E.  g., 

"With  taper  light 
To  seek  the  beauteous  eye  of  heaven  to  garnish  {=mibject) 
Is  {=copula)  wasteful  and  ridiculous  excess  "  (—predicate). 

§  60.  A  judgment  always  expresses  the  relation 
of  two  notions  now  in  mind ;  therefore  the  copula 
must  always  appear  as  the  present  tense  of  the 
verb  to  he :  For  the  mind  is  its  own  kingdom,  in 
which  an  eternal  now  does  always  last.  Yery  often 
in  common  speech  it  is  absorbed  in  verb  forms, 
or  elided,  and  a  whole  proposition  may  be  ex- 
pressed by  a  single  word.  E.  g.,  Stars  twinhle^ 
i.  e.  Stars  are  things  that  twinkle  /  He  loved,  i.  e.  He 
is  one  who  loved;  Cogito,  i.  e.  /am  thinking  /  Ilium 
fuit,  i.  e.  Troy  was,  i.  e.  Troy  is  something  that  for- 
merly existed  (existential) ;  Did  he  say  so  ?  Ans. 
Yes,  i.  e.  He  is  one  who  said  so.  All  verbs  are  per- 
haps fundamentally  one,  the  verb  to  he  of  the  sum- 
mum  genus  heing,  their  variety  arising  from  the  in- 
corporation of  various  temporal  and  attributive  no- 
tions with  this  simple  verbal  element,  its  own  past 
and  future  forms  being  adverbial  notions  incorpo- 
rated with  its  present  tense. 

The  copula  admits  of  only  one  qualification,  ne- 
gation.    Hence  in  a  negative  proposition  the  nega- 


70  CONCEPTION 

tive  particle,  wherever  it  may  occur,  is  a  part  of 
the  copula.  E.  g.,  The  quality  of  jnercy  is  not 
st/rained;  No  chastisement  is  joyous^  Not  a  drum 
was  heard;  Not  every  mistake  is  culpable;  Britan- 
nia needs  no  bulwark,  i.  e.  Britannia  is  not  needing 
a  bulwark. 

Let  it  be  observed  that  affirmative  propositions 
often  contain  negatives  in  the  subject  or  in  the 
predicate,  and  should  not  be  mistaken  for  negative 
propositions.  E.  g.,  To  wonder  not  is  a  rare  art; 
Axioms  affi/rm  what  no  one  can  deny.  Also  observe 
that  propositions  affirmative  in  form  are  sometimes 
negative  in  thought.  E.  g.,  The  brute  perishes;  He 
is  blind;  Darkness  and  silence  fall  on  land  and  sea. 
Negative  thought  may  also  be  conveyed  in  affirm- 
ative forms  by  means  of  such  words  and  phrases 
as  ^£^^Aoi^i^ ^^0B^4^«2L^f om^ iAe  reverse ^of  on  t/ie 
contmr^ljjwam^ 
like.     E.  g.,  We  can  do  without  it. 

I     §  61.   In  accordance  with  its  postulate  (§  13), 
i  logic  requires  that  all  propositions  shall  be  trans- 
formed, as  has  been  shown,  so  that,  without  addi- 
'  tion  or  retrenchment  or  distortion  of  the  thought, 
the  three  parts,  subject,  copula,  predicate,  shall 
1  severally  appear.     The  process  is  sometimes  quite 
.  troublesome,  and  the  result  awkward,  but  it  is  nev- 
ertheless indispensable.     E.  g..  So  he  said  becomes 
What  has  just  been  said  is  what  he  said ;  If  he 
should  come  to-morrow,  he  will  probably  stay  till 
Monday  becomes  The  happening  of  his  arrival  to- 


SIMPLE   PROPOSITIONS  71 

morrow  is  an  event  from  which  it  may  he  inferred 
as  probable  that  he  loill  stay  till  Monday. 

The  proposition  often  exhibits  rhetorical  inver- 
sions, and  a  displacement  of  minor  parts.  E.  g., 
Great  is  Diana  of  the  Ephesians  /  Few  and  short 
were  the  prayers  we  said  /  Flashed  all  their  sabres 
bare  /  Gold  and  silver  ha/oe  I  none  /  but  what  I 
have,  that  give  I  thee.  Herein  order  must  be  re- 
stored, the  subject  naturally  coming  first. 

All  inversions  and  displacements  corrected,  all' 
elisions  supplied,  and  the  three  parts  stated  dis- ' 
tinctly  in  their  natural  order,  constitute  the  re-  j 
duction  of  a  proposition  to  its  strict  logical  form.] 
Hence  every  proposition  must,  for  logical  purposes, 
be  reduced  to  one  or  the  other  of  the  two  invaria- 
ble forms,  S  is  P,  or  S  is  not  P. 

§  62.  It  has  already  been  stated  that  proposi- 
tions, as  to  their  Quality,  are  positive  and  negative 
(§  51).  It  is  now  to  be  observed  that  propositions, 
as  to  their  Quantity,  are  total  and  partial.  The 
quantity  of  a  judgment  or  proposition  is  determined 
solely  by  the  quantity  of  its  subject,  according  as 
this  is  definite  or  indefinite.  The  following  scheme 
exhibits  this  division  with  subdivisions : 

r Total,  definite. . .  ri"d««^"al,  as,  All  the  world's  a  stage. 

„         ., .  I  Universal,  as.  All  men  are  players. 

Propositions  i  L  '     '  "^   •' 

p     .  .   .    ,  ~  .     j  Divisive,  as,  Some  play  soldier. 
1  Indivisive,  as,  Some  act  armies. 

The  quantity  of  the  subject,  and  hence  of  the  prop- 
osition, is  indicated  by  the  predesignation  all  or 


C 


72  CONCEPTION 

some,  or  its  equivalent.  These  two  exhaust  the 
possibilities  of  predication;  that  is  to  say,  every 
possible  proposition  predicates  either  concerning 
all,  or  concerning  some,  of  its  subject. 

It  is  often  the  case  that  ;io  sign  of  quantity  is 
prefixed.  A  judgment  always  has  quantity  in  the 
mind  of  the  thinker  and  speaker,  but  the  hearer 
may  be  left  to  surmise  the  quantity  from  the  mat- 
ter or  the  context.  E.  g.,  Birds  'breathe,  i.  e.  all  do, 
the  predicate  being  of  the  essence ;  Birds  sing,  i.  e. 
some  do,  the  predicate  being  an  accident.  On  re- 
ducing such  propositions  to  strict  logical  form,  it  is 
generally  needful  to  designate  the  quantity  by  its 
sign. 

^1  §  63.  Indivi_dual  propositions  are  those  in  which 
the  subject  is  thought  as  an  indivisible  total.  The 
subject  may  be  a  proper  noun,  as  in  Coesar  is  amM- 
■  tious  /  or  something  designated  by  the  definite  ar- 
ticle, or  any  demonstrative  or  possessive,  as  in  The 
world  is  round.  This  man  is  crazy,  Let  your  words 
be  few.  It  may  be  a  collective  whole,  as  in  The 
college  of  apostles  was  typified  in  the  twelve  tribes 
(§  24).  It  may  even  be  a  genus,  as  in  The  horse  is 
a  noble  am,imal.  It  may  be  unified  by  all,  as  in 
All  Jerusalem  went  out  to  meet  him.   -  . 

^1/  §  64.  Univfirsal  propositions  are  those  in  which 
the  subject  is  thought  as  a  divisible  total.  The 
subject  is  said  to  be  distributed,  because  what  is 
said  of  it  as  a  whole  is  thought  as  distributively 


SIMPLE    PROPOSITIONS  73 

applicable  to  each  part,  as  in  All  men  are  players, 
i.  e.  all  without  exception ;  and  in  Every  man  is  a 
player,  i.  e.  each  taken  severally.  So  also  in  iVb 
man  is  perfect. 

Predesignations  or  signs  of  universality  or  dis- 
tribution are  all,  a  or  an  or  every,  each,  hoth,  neither, 
not  any,  none,  always,  never,  whoever,  etc. 

It  appears  that  all  is  ambiguous,  meaning  either 
all  as  an  undistributed  unity,  or  all  as  a  distributed 
plurality,  as  in  Drink  ye  all  of  it.  The  matter 
generally  determines  whether  the  meaning  is  cu- 
mular  or  distributive. 

Names  of  substances,  as  water,  flesh,  flame,  iron' 
of  forces,  as  gravity,  heat ;  of  actions,  as  to  walk, 
talking',  and  abstract  terms,  as  ehartty,  are  usually 
universal  without  predesignation. 

§  65.  Partial  or  indefinite  propositions  are  those 
in  which  the  subject  is  thought  as  less  than  the 
whole  denoted  by  its  naked  form.  We  do  not 
think  definitely  of  all,  but  partially  or  particularly 
of  some.  The  indefinite  some,  as  the  predesigna- 
tion of  logical  quantity  in  affirmative  propositions, 
means  at  least  some,  perhaps  all ;  in  negatives,  it 
means  at  least  some  not,  perhaps  none.  E.  g..  Some 
men  play  soldier,  i.  e.  at  least  some,  perhaps  all,  do ; 
Some  m&n,  are  not  pure,  i.  e.  at  least  some  are  not, 
perhaps  none  are.  A  subject  thus  quantified  is  said 
to  be  undistributed. 

Predesignations  or  signs  of  particular  or  indefi- 
nite propositions  are  some,  a  few,  a  or  an  or  one,  two, 


74  CONCEPTION 

three,  etc.,  certain,  there  are — that,  not  all,  not  every, 
sometimes,  somewhere,  etc.  E.  g,,  A  few  are  saved, 
i.  6.  some,  a  small  number,  are,  perhaps  all ;  There 
are  men  that  practise  self-denial,  i.  e.  some  exist,  at 
least  a  few,  perhaps  many,  perhaps  all ;  All  are  not 
here,  i.  e.  some  are  not  here,  contradicting  All  are 
here ;  Not  every  step  counts,  i.  e.  some  steps  do  not 
count.  The  sign  any  signifies  an  indifferent  some ; 
the  statement  is  limited  to  some,  but  is  applicable 
to  every  one,  as  in  Anyhody  can  do  that. 

There  are  signs  that  approximate  the  total,  but 
being  less  are  still  particular,  as  many,  most,  almost 
all,  tfie  large  majority  of,  etc.  Others  are  nearly 
total  negatives,  as/e?^,  very  few,  hardly  or  scarcely 
any,  little,  small,  slight,  rare,  seldom,  etc.  E.  g.. 
Many  are  called,  hut  few  chosen,  i.  e.  at  least  some, 
nearly  all,  perhaps  all  are  called,  but  at  least  some 
are  not,  nearly  none,  only  a  few,  chosen ;  Few  are 
saved,  i.  e.  many  are  not,  perhaps  none  ;  Little  reck 
I,  i.  e.  almost  and  may  be  not  at  all.  Let  it  be 
remarked  that  a  few  and  a  little  are  affirmative, 
and  that  not  all,  when  cumular,  is  total. 

§  66.  It  appears  that  some  also  is  ambiguous. 
Besides  the  divisive  sense  just  considered,  it  has  an 
indivisive,  undistributed  sense.  E.  g..  Some  men 
act  armies,  means  that  a  portion,  a  section,  wholly 
indefinite  as  to  extent,  do  so.  It  has  the  same 
meaning  in :  Give  one  some  water  /  Some  tiine  has 
passed;  We  have  come  some  distance;  Some  of  the 
way  was  rough;  Some  of  the  company  is  i/n  ad- 


SIMPLE    PKOrOSlTIONS  75 

vance.  The  thought  is  of  a  mathematical  quantity, 
of  a  mass,  logically  indivisible  (§  24). 

Besides  its  indefinite  significations,  some  is  often 
used  in  a  semi-definite  sense,  meaning  some  at  most, 
not  all,  as  in  Some  m,en  seekfajne,  i.  e.  some  at  most 
do,  but  not  all,  for  some  do  not.  This  form,  how- 
ever, is  compound,  and  will  be  examined  in  the 
next  chapter  (§  72). 

§  67.  Combining  the  quality  and  quantity  of 
propositions,  and  symbolizing  by  vowels,  we  have 
the  following  scheme  of  the  four  simple  proposi- 
tional  forms : 

Quantity.        Qaality.    Symbol       Formula.  Example. 

Universal  Affirmative, — A — All  S  is  P All  oaks  are  exogens. 

Universal  Negative,     — E — No  S  is  P No  oaks  are  vines.  i 

Particular  Affirmative, —  I  — Some  S  is  P Some  oaks  are  trees.         ~^ 

Particular  Negative,    — 0 — Some  S  is  not  P. .  .Some  are  not  shrubs. 

The  examples  are  in  strict  logical  form.  Indi- 
vidual propositions  (§  63),  since  the  subject  is  def- 
inite, are  treated  as  universals,  and  symbolized  by 
A  and  E.  Propositions  whose  subject  is  the  indi- 
visive  some  (§  Q^),  being  indefinite,  may  be  symbol- 
ized by  I  and  O. 

§  68.  A  simple  proposition  comprises  only  one 
judgment ;  it  contains  not  more  than  one  subject 
and  one  predicate.  It  may,  however,  consist  of 
many  grammatical  elements ;  as,  Well  -  orgam^ized 
a/ad  skilfully  adm^inistered  governments  are  jprodnc- 
tive  of  hapj}i7iess  in  their  subjects. 


76  CONCEPTION 

A  complex  proposition  involves  witb  the  princi- 
pal judgment  one  or  more  subordinate  judgments. 
This  subordinate  element  appears  as  a  clause  inci- 
dental to  the  principal  subject  or  predicate.  E.  g., 
A  man  who  is  learned  is  respected ;  I  am  monarch 
of  all  /  survey ;  They  that  are  wise  shall  shine  as 
the  stars  {shine). 

A  subdivision  may  be  made  into  explicative  and 
restrictive  clauses.  The  explicative  clause  merely 
unfolds  the  marks  connoted  by  the  notion  it  quali- 
fies ;  as,  Man,  who  is  horn  of  woman,  is  of  few  days. 
The  restrictive  clause  limits  the  notion  it  qualifies ; 
as,  111  blows  the  wind  that  profits  nobody.  Not  all 
winds,  but  all  in  a  limited  class,  are  here  spoken  of. 
The  concessive  clause  removes  a  conceivable  re- 
striction ;  as,  I  will  trust  him  though  he  slay  me. 
When  a  restriction  is  a  condition,  the  categorical 
may  be  transformed  to  a  conditional  proposition ; 
thus,  A  man  who  is  learned  is  respected,  becomes, 
If  a  man  be  learned,  he  is  respected. 

Now,  be  it  observed  that  the  complex  proposition 
is  treated  logically  as  a  simple  proposition,  the  in-- 
cidental  clauses  being  regarded  as  mere  substan- 
tive, adjective,  or  adverbial  qualifiers.  In  reducing 
to  strict  logical  form,  it  is  needful  to  subordinate 
clauses  to  the  principal  subject  and  predicate,  and 
to  place  them  in  close  connection  with  the  notions 
they  qualify ;  as.  He  who.,  though  he  he  rich,  is  sa/o- 
ing  is  one  that  can  share  with  him  who  is  needy 
without  lessening  what  is  enjoyed ;  here  the  form 
is  simply,  S  is  P.     Indeed,  the  complex  proposition 


SIMPLE    PROPOSITIONS  77 

is  often  directly  reducible  to  one  that  is  strictly 
simple ;  thus,  The  man  who  is  learned  is  respected, 
becomes,  The  learned  man  is  respected. 

This  account  of  the  complex  proposition  is  given 
to  prevent  clauses  from  being  mistaken  for  princi- 
pal propositions,  and  so  confusing  it  with  the  com- 
pound proposition. 

§  69.  Praxis.  Concerning  each  of  the  follow- 
ing propositions,  answer,  in  their  order,  these  five 
questions :  Is  it  conditional  or  categorical  ?  If 
categorical,  what  is  its  strict  logical  form  ?  What 
is  its  symbol  of  quantity  and  quality  ?  Is  it  indi- 
vidual ?  Aside  from  its  form,  is  it  essentially  posi- 
tive or  negative? 

1.  No  man  is  wiser  because  of  his  learning. 

2.  The  senate  has  adjourned.     Charity  affords  relief. 

3.  If  you  understand  this,  you  can  explain  it. 

4.  From  peak  to  peak  the  rattling  crags  among 
Leaps  the  live  thunder. 

5.  There  was  a  sound  of  revelry  by  night. 

6.  This  to  hear 
Would  Desdemona  seriously  incline. 

7.  Not  to  know  me  argues  yourself  unknown. 

8.  I  implore  you,  reject  not  this  bill, 

9.  The  blind  are  helpless.     Richard  III.  was  infamous. 
10.  Men  are  all  sinners.     No  news  is  good  news. 

.11.  Few  patriots  are  disinterested.    Diogenes  was  no  fool. 

12.  All  these  claims  upon  my  time  overpower  me. 

13.  Virtue  is  teachable,  if  it  be  knowledge. 

14.  Not  many,  if  any,  metals  are  without  lustre. 


78  CONCEPTION 

15.  Not  being  rich  is  not  always  an  evil. 

16.  Hardly  any  virtue  is  safe  from  passing  into  vice. 

17.  Those  here  present  constitute  the  class  in  logic. 

18.  There's  few  or  none  do  know  rae.     That  horse  won 

the  race.     A  general  cry  was,  No  surrender. 

19.  There  are  who  ask  not  if  thine  eye  be  on  them. 

20.  I  will  not  let  thee  go,  unless  thou  bless  me. 

21.  The  most  skilful  general  was  Napoleon. 

22.  Little  preface  is  needed.    Not  every  man  is  honest. 

23.  The  circle  is  the  figure  of  greatest  area. 

24.  Some  education  is  desirable.    Some  pudding,  a  slice, 

if  you  please.     Some  love  to  roam. 

25.  All  honorable  conduct  is  not  to  be  rewarded. 

26.  Yonder  forest  is  a  covert  for  outlaws. 

27.  Gold  is  precious.     To  converse  is  pleasant. 

Eeduce  each  of  the   following  propositions  to 
strict  logical  form,  and  affix  its  symbol : 

28.  Nothing  is  harmless  that  is  mistaken  for  virtue.   ^■-» 

29.  One  truth  is  clear,  whatever  is,  is  right.        ^Z^ 

30.  All  is  not  gold  that  glitters.  Lo  \ 
•  81.  He  who  truly  loves  most  is  not  he  who  flatters.  ^C^  j 

32.  Though  this  be  madness,  yet  there's  method  in  it. 

33.  Even  a  fool  is  counted  wise,  when  he  holdeth  his 

peace.     That  I  am  is  no  proof  that  he  is. 

34.  They  strive  that  they  may  enter  in. 

35.  There's  a  divinity  that  shapes  our  ends, 
Rough-hew  them  how  we  will. 


Vni— COMPOUND   PROPOSITIONS 

§  70.  A  compound  proposition  is  one  that  com- 
prises two  or  more  judgments,  co-ordinate  or  near- 
ly so.  For  logical  treatment  the  components  are 
to  be  separated,  and  stated  independently.  Such 
propositions  are  of  two  kinds,  according  as  the 
composing  elements  are  more  or  less  obvious. 

The  first  kind,  wherein  the  components  are  quite 
obvious,  has  received  no  specific  name,  and  needs 
only  a  few  illustrations.  E.  g..  Art  is  long,  and 
time  is  fleeting;  Every  man  desireth  to  live  long,  hut 
no  man  would  he  old.  In  Yeni,  vidi,  vici,  there  are 
three  propositions.  So  also  in  Pompey,  Crassus, 
and  CcBsar  were  triumvirs.  It  is  often  the  case 
that  a  simple  proposition  has  a  compound  subject 
or  predicate,  as  in  Pompey,  Crassus,  and  Ccesar 
were  the  triumvirs,  for  the  three  are  here  taken  col- 
lectively as  one  whole.  So  Roses  and  lilies  contend 
for  a  home  in  her  cheeh  is  single  and  simple ;  but 
in  Darkness  and  silence  settle  on  land  and  sea  there 
are  four  propositions. 

§  71.  Compound  propositions  of  the  second  class, 
having  components  less  obvious,  require  analysis, 
and  are  called  exponibles.  They  are  chiefly  ex- 
clusives  and  exceptives. 


80  CONCEPTION 

Exclusives  may  be  formulated  and  exemplified 
thus: 

o  .     A  •    R       <  AisB A  or  I 

^"'y^"^  =  -lNon-Ai9notB E  or  O 

Faith  justifies A 

E.  g.,  Faith   alone  justifies  =  ^  What  is  not  faith  does  not 


I  faith  justifies 
What  is  not  faith  does  not  ) 
justify \ 


E 


It  is  evident  that  this  proposition  may  be  in- 
verted and  the  excluding  particle  made  to  appear 
in  the  predicate ;  thus,  Justification  is  by  faith 
alone,  i.  e.  B  is  only  A. 

Exceptives  are  exemplified  in  All  hut  one  were 
saved,  which  means  Nearly  all  were  saved,  and  One 
was  not  saved,  I  and  O.  It  should  be  noted  that 
hut  is  sometimes  not  exceptive,  but  merely  adver- 
sative, as  herein  ;  also,  that  it  sometimes  means 
that — not,  as  in  It  cannot  he  hut  nature  hath  some 
director. 

No  useful  rule  can  be  given  for  the  resolution  of 
these  exponibles.  The  components  differ  in  quali- 
ty, and  one  is  direct  and  the  other  implied.  But 
the  distinction  between  exclusives  and  exceptives 
is  of  no  logical  moment,  for  they  are  mutually  con- 
vertible, the  difference  being  that  what  is  the  di- 
rect judgment  in  the  one  form  becomes  the  indirect 
in  the  other. 

The  following  are  some  of  the  exclusive  and  ex- 
ceptive particles :  onh^,  alor^,  m&rely,  solely,  save, 
hut,  etc.  These  particles,  when  qualifying  a  uni- 
versal subject,  quantify  the  predicate  totally;  as, 
Ood  alone  is  wise,  i.  e.  He  is  all  the  wise.  When 
qualifying  the  entire  predicate,  they  limit  the  sub- 


COMPOUND   PROPOSITIONS  81 

ject  to  that  predicate ;  as,  The  sacraments  are  hut 
two,  i.  e.  there  are  no  more.  Sometimes  the  ex- 
clusion or  exception  is  in  the  sense,  and  not 
expressed;  as,  {There  is  only)  one  Lord,  onefaith^ 
one  baptism. 

§  72.  Our  thoughts  are  often  incompletely  ex- 
pressed. A  proposition  may  be  accompanied  by 
another  limiting  judgment  unexpressed,  with  no 
sign  of  implication,  yet  understood,  because  of  our 
knowledge  of  the  matter.  Thus  if  we  say,  Som.e 
flowers  are  fragrant,  knowing  very  well  that  some 
are  not,  the  proposition  is  accompanied  by  the 
counter-judgment.  Some  flowers  are  not  fragrant. 
If  this  double  thought  be  completely  expressed  in 
a  single,  grammatically  simple  proposition,  it  is, 
Only  some  flowers  are  fragrant.  IS^ow,  this  formt 
is  an  exponible,  a  logical  compound,  which  an- 
alyzes into  the  two  logically  simple  propositieas : 

Some  flowers  (I  know  not  bow  many)  are  fragrant I 

Some  flowers  (I  know  not  how  many)  are  not  fragrant ® 

Each  of  these,  considered  in  itself,  entirely  apart 
from  the  other,  is  wholly  indefinite ;  for  the  mean- 
ing of  some,  I  know  not  how  many,  must  in  that 
case  be  at  least  some,  perhaps  all.  It  is  evident, 
then,  that  some,  in  the  semi-definite  sense  of  some 
at  most,  not  all  (§  66),  is  equivalent  to  only  some, 
and  does  not  occur  unless  one  judgment  is  thought 
as  limiting  another.  Therefore,  propositions  quan- 
tified by  the  so-called  semi-definite  som^  are  com- 
pound propositions. 


82  CONCEPTION 

Since  logic  proposes  to  exhibit  a  thorough  anal- 
ysis of  thought,  it  should  in  no  case  stop  short 
of  simple  forms.  It  is  out  of  character  to  present 
compound  forms  as  the  result  of  analysis,  and 
especially  to  rank  them  as  co-ordinate  with  simple 
forms.  Hence  the  semi-definite  proposition  must 
be  denied  a  position  among  the  elementary  forms, 
and  assigned  a  place  among  the  abbreviated,  ellip- 
tical modes  of  statement,  subject  to  analysis  and 
full,  discrete  expression. 

§  73.  The  predicate  of  a  simple  qualitative  prop- 
osition has  no  quantity  whatever.  We  mean  to 
say,  not  merely  that  it  may  have  none,  but  that  it 
cannot  possibly  have  any.  This  is  quite  obvious  in 
case  of  intensive  propositions.  E.  g..  An  athlete  is 
strong,  cannot  mean  either  all  strong  or  some  strong , 
which  is  senseless,  but  simply  that  the  mark  strong 
is  found  in  the  subject.  In  case  of  negative  prop- 
ositions, both  intensive  and  extensive,  the  same  is 
true.  E.  g..  Some  athletes  are  not  studious,  or  are 
not  students,  means  simply  to  deny  the  notion 
studious  or  students  of  the  subject,  without  any 
quantification  of  students.  The  subject  and  predi- 
cate are  merely  coexclusive.  The  same  is  equally 
true,  though  perhaps  nofr  so  clearly  evident,  in  case 
of  affirmative  propositions  in  extension.  E.  g.,  AU 
athletes  are  sportsmen,  or  Some  athletes  are  snobs, 
merely  places  athletes  in  a  class,  without  any 
thought  whatever  of  the  quantity  of  the  class; 
that  is,  without  thinking  it  as  either  all  or  some. 


COMPOUND   PROPOSITIONS'  83 

The  statement  that  a  predicate  cannot  have 
quantity  is  true  of  simple  qualitative  propositions 
only.  We  can  readily,  and  often  do,  think  quan- 
tity into  the  predicate  of  extensive  propositions; 
but  this  is  to  compound  our  thoughts,  the  pred- 
icate becoming  for  a  moment  the  subject  of 
thought,  and  then  being  restored  to  its  place 
quantified.  For  example,  if  we  say.  All  triangles 
are  trilaterals,  and  then  think  that  All  tr Hater als 
are  triangles^  we  may  express  the  double  thought 
directly  thus:  All  triangles  are  all  trilaterals.  It 
has  already  been  remarked  that  an  exclusive  or  an 
exceptive  added  to  a  universal  subject  quantifies 
the  predicate  totally  (§  71),  and  so  the  same 
thought  may  be  indirectly  expressed  by  the  ex- 
ponible.  Only  triangles  are  trilaterals.  In  like  man- 
ner predicates  of  other  forms  may  be  quantified. 

A  very  convenient  mode  of  symbolizing  the 
forms  of  such  propositions  has  been  devised,  which 
we  shall  have  some  occasion  to  use.  Let  a  stand 
for  a  total,  i  for  a  particular  term ;  also  let  f  repre- 
sent the  aflBrmative,  and  n  the  negative  copula. 
Then  the  forms  spoken  of  may  be  represented 
thus: 

All  triangles  are  (all)  trilaterals aM  are  aM afa 

All  triangles  are  (some)  figures all  are  some afi 

Some  men  are  (all)  priests some  are  all ifa 

Some  men  are  (some)  poets some  are  some ifi 

Some  men  are  not  (any)  poets some  are  not  any ina 

No  oaks  are  (any)  vines not  any  are  any ana 

§  74.  Two  views  may  be  taken  of  these  forms. 


84  XJONCEPTION 

With  reference  to  their  origin,  they  are  compound 
propositions,  formed  from  components,  into  which 
they  can  be  resolved.  In  this  view,  they  cannot 
be  allowed  co-ordinate  rank  with  the  four  simple 
forms  (§  67),  and  must  be  held  subject  to  analysis. 

If  viewed  in  themselves,  without  reference  to 
their  origin,  they  are  seen  to  be  propositions,  not 
in  the  qualitative,  but  in  the  quantitative  whole 
(§  23).  For  consider  the  meaning  of  afa.  Take, 
All  men  are  all  himana.  Here  the  ambiguous  all 
(§  64)  has  changed  from  the  distributive  all,  which 
quantifies  the  components,  to  the  cumular,  indivisi- 
ble all  (§  63).  It  does  not  mean,  Every  man  is  every 
himana,  which  is  nonsense,  but  All  men  (taken  to- 
gether as  a  mass)  =  all  himana  (taken  together  as 
a  mass).  The  proposition,  considered  in  itself,  is 
therefore  a  mathematical  equation.  This  is  clearly 
true  of  the  affirmative  forms.  As  to  negative  forms, 
any  thought  into  the  predicate  does  not  properly 
quantify  it,  but  serves  rather  to  emphasize  the  nega- 
tion, the  proposition  remaining  qualitative ;  though, 
of  course,  a  mass  may  be  denied  of  a  mass,  and  we 
may  think  a  negative  proposition  in  either  whole. 

Wh[le,  therefore,  a  simple  qualitative  judgment 
always  has  a  quantified  subject,  it. cannot  have  a 
quantified  predicate.  It  follows,  also,  that  a  system 
of  logic  built  upon  the  quantification  of  the  predi- 
cate is  vicious,  either  by  confusing  compound  with 
simple  forms,  or  else  by  unnaturally  transferring 
all  thought  to  the  quantitative  whole,  and  so  mak- 
ing logic  merely  a  branch  of  applied  mathematics. 


COMPOUND   PKOPOSITIONS  85 

§  75.  Finally,  it  is  to  be  observed  that  in  draw- 
ing inferences,  and  so  transforming  thought,  it  is 
frequently  necessary  to  make  a  predicate,  for  a  mo- 
ment at  least,  the  subject  of  a  judgment  to  which 
quantity  is  assigned.  Then  this  is  spoken  of  as  the 
quantity  of  the  predicate,  and  must  be  taken  into 
account  in  many  forms  of  illation.  Now,  this  so- 
called  distribution  of  the  predicate,  ascertained  by 
compounding  the  thought,  and  having  no  verbal 
sign,  depends  on  the  quality  of  the  judgment,  and 
is  expressed  by  the  following  Eule  :  Negatives 
distributejbhe  predicate,  affirmatives  do  not. 
~In  view  of  the  preceding  discussion,  it  is  clear 
that  this  statement  taken  in  itself  as  to  simple  judg- 
ments is  not  true.  But  taken  merely  as  a  derived 
rule  to  be  applied  in  illation,  tersely  and  hence  im- 
perfectly expressed,  it  serves,  under  the  given  ex- 
planation, as  an  unerring  guide  in  logical  processes. 

§  76.  Praxis.  Keferring  to  each  of  the  follow- 
ing propositions  by  its  number,  state  whether  it  be 
simple,  complex,  or  compound.  If  either  of  the  two 
former,  reduce  it  to  strict  logical  form,  and  affix 
the  capital  symbol  (§  67).  If  compound,  state  what 
kind,  then  write  its  components,  affixing  to  each  the 
capital  symbol,  and  noting  the  semi-definite  so7ne. 
If  its  predicate  have  a  sign  of  quantity,  symbolize 
literally  (§  73),  then  state  its  components  with  their 
capital  symbols. 

1.  None  but  the  brave  deserve  the  fair. 

2.  Mercy  but  murders,  pardoning  those  that  kill. 


86  CONCEPTION 

3.  Men  may  come,  and  men  may  go, 
But  I  go  on  forever. 

4.  Length,  breadth,  and  depth  are  all  the  dimensions  of 

extension. 
6.  When  I  was  a  boy,  I  always  chose  the  wrong  side. 

6.  It  is  the  duty  of  every  man  to  fear  God  and  honor 

the  king. 

7.  Jonah  sought  to  evade  the  God  who  is  omnipresent. 
^:/      8.  Few,  few  shall  part  where  many  meet, 

The  snow  shall  be  their  winding-sheet. 
9.  There  is  no  fireside,  howsoe'er  defended, 
But  has  one  vacant  chair. 
^■^   10.  Not  every  one  that  saith  unto  me,  Lord,  Lord,  shall 

enter  in,  but  he  that  doeth  the  will  of  my  Father. 
/^   11.  Some  inspired  men  were  all  of  the  apostles. 
/■'Z>    12.  Brutus,  in  killing  Caesar,  was  merely  patriotic. 
xyjy  13,  The  moon  is  only  our  satellite. 
J-'/.  14.  The  moon  is  our  only  satellite. 
-''  /-  15.  The  paths  of  glory  lead  but  to  the  grave. 
16.  A  fool  thinks  none  except  himself  wise. 
1*7.  Ho  !   hearts,  tongues,  figures,  scribes,  bards,  poets, 
cannot 
Think,  speak,  cast,  write,  sing,  number — hoo ! — 
His  love  to  Antony. 

18.  Live  how  we  can,  yet  die  we  must. 

19.  Some  who  are  poor  are  nevertheless  contented. 

P/^    20.  All  grace  is  all  free  favor.     Certain  gifts  are  not  any 

favor. 
J^  21.  All  present  are  some  of  my  friends. 
/  ■Z'22.  My  tasks  are  all  but  impossible. 

23.  The  quarrel  toucheth  none  but  us  alone. 
/''^24.  Whereto  serves  mercy,  but  to  confront  the  visage  of 

oflfence  ? 


PART  II.— DEDUCTION 

I.— IMMEDIATE    INFERENCE    ^ 

§  77.  A  judgment  either  aflBrms  or  denies  that 
one  notion  is  in  orunder  another  (§  58).  A  division 
of  judgments,  grounded  on  the  process  by  which 
they  are  formed,  is  as  follows : 

!  Intuitions. 
(   Inductive. 
Inferences.    •<  C  Immediate. 

(  Deductive.    -< 

(  Mediate. 

Intuitions  are  self-evident,  axiomatic  judgments. 
They  are  the  origin  of  all  knowledge,  and  deter- 
mine all  other  judgments;  for  example,  the  Pri- 
mary Laws  (§  7  sq.). 

Inferences  are  enunciations  in  which  from  some- 
thing laid  down  and  admitted,  something  distinct 
fromj;vhat  is  laid  down  follows  of  necessity.  Or, 
more  simply,  to  infer  is  to  derive  a  judgment  from 
one  or  more  premised  judgments.  Both  the  process 
and  the  conclusion  are  called  inferences. 

Inductive  inferences  are  universal  judgments  de- 
rived  from  particular  cases,  and  furnishing  premises 
for  subsequent  deduction.  The  general  definition 
of  Logic  includes  them  (§  6),  but  the  present  work 


88  DEDUCTION 

is  limited  to  deductive  inferences.    Inductive  Logic 
requires  a  separate  treatise. 

Deductive  inferences  are  judgments  of  equal  or 
less  generality  thanjhe  premises  from  which  they 
are  derived.  They  are  especially  the  subject  of 
Deductive  Logic,  and  are  of  two  kinds,  immediate 
and  mediate. 

When  two  notions  having  a  given  relation  are 
concluded  of  each  other  in  another  reration  witE^ 
out  the  introduction  of  a  third  notion,  the  inference 
is  immediate.  In  this  case  one  judgment  is  derived 
dTrectly  from  another.  The  conclusion  has  but  one 
premise,  the  given  judgment.  The  matter  in  both 
is  the  same ;  the  relation  is  modified. 

A  mediate  inference  or  a  reasoning  is  accom- 
plished through  a  third  notion  used  as  a  medium  of 
comparison.     It  has  two  premises. 

§ '78.  Implications  should  be  distinguished  frpjn 
inferences.  An  implied  judgment  is  one  actually 
coexisting  with  the  given  judgment,  either  merely 
in  thought  or  involved  covertly  in  the  expression. 
An  inferred  judgment  is  one  that  only  potentially 
exists  in  the  given  judgment,  and  may  be  derived 
from  it.  The  statement  of  the  one  is  nothing  new, 
there  is  no  advance,  no  progress  of  thought,  but 
only  its  full  expression ;  that  of  the  other  contains 
something  new,  there  is  a  step  forward,  a  progress 
of  thought. 

The  forms  extension  and  intension  are  hardly  to 
be  considered  even  as  implying  each  other,  much 


IMMEDIATE   INFERENCE  89 

less  as  inferable  one  from  the  other.  They  are 
simply  different  aspects  of  the  thought,  which  nec- 
essarily coexist,  one  having  merely  accidental  pre- 
ponderance (§  20). 

Correlatives  merely  imply  and  are  not  inferable 
from  one  another  (§  30).  To  infer  from  The  cause 
of  the  explosion  was  a  spark,  that  The  effect  of  a 
spark  was  the  explosion,  is  a  fallacy  (§  146). 

The  interchange  of  active  and  passive  forms  is 
not  an  inference.  Ood  made  the  world,  and  The 
world  was  made  hy  God,  imply  each  other,  or  rather 
are  equipollent  (§  13). 

Incomplete  speech  implies  thought,  as  in  the 
semi-definite  proposition  (§  72).  Thus  if  we  say. 
Some  men  are  rich,  it  is  accompanied  by  the  judg- 
ment that  Some  men  are  not  rich.  But  this  actually 
coexistent  thought  is  not  inferred.  "We  cannot  say 
that  from  Soine  men  are  rich,  it  follows  that  some 
are  not.  An  exponible  contains  an  implied,  indi- 
rect judgment  covertly  expressed,  as  in  Only  some 
men  are  rich. 

Finally,  neither  the  compounding  of  two  or  more 
simple  propositions,  nor  the  resolution  of  a  com- 
pound proposition  into  its  components,  should  be 
mistaken  for  inference. 

§  79.  Also  preparatory  to  an  account  of  the  sev- 
eral kinds  of  immediate  inference  for  which  we 
shall  have  subsequent  use,  we  state  a  prohibition 
applied  to  all  deductions  in  the  following  Kule: 
The  quantiflcation  must  not  be  increased. 


90  DEDUCTION 

Truly  we  may  deduce  all  from  all,  some  from  some, 
soine  from  all,  but  not  all  from  some.  It  is  evident 
that  what  is  said  only  of  soms  furnishes  no  ground 
for  a  deduction  concerning  all.  The  attempt  to 
make  this  deduction  in  violation  of  the  foregoing 
rule  is  called  the  illicit  process.  The  principles 
of  induction  license  the  inference  of  all  from  soms, 
and  so  exhaust  the  possible  processes. 

§  80.  Determination.  Immediate  inference  by 
determination  is  one  of  the  four  kinds  to  be  noted. 
The  same  mark  may  be  added  to  both  terms  of  a 
proposition,  by  which  they  are  more  closely  deter- 
mined (§  42),  The  new  judgment  thus  formed  is 
an  immediate  inference  from  the  given  premise. 
Thus,  from  Coal  is  fuel,  it  follows  that  Cheap  coal 
is  cheap  fuel  j  if  Science  he  system,  then  A  false 
science  is  a  false  system.  We  must  be  on  our  guard 
not  to  use  a  determinant  ambiguously,  as  in  A  king 
is  a  man,  therefore  A  good  king  is  a  good  man. 
The  narrowing  of  both  subject  and  predicate  by 
thinking  a  mark  into  them  is  passing  from  genus 
to  species.  We  observe  that  the  subtraction  of  the 
same  mark  from  both  terms  is  legitimate ;  but  the 
remainder  is  an  implicit  judgment,  not  an  infer- 
ence. 

Inverting  the  foregoing  process,  the  two  terms 
of  a  proposition  may  be  added  as  marks  to  the 
same  concept.  Thus,  if  Science  he  system,  then  A 
scientific  a/rrangement  is  a  systematic  arrangement. 
Also  two  propositions  may  be  combined,  the  terms 


IMMEDIATE    INFERENCE  91 

of  one  being  added  as  marks  to  the  terms  of  the 
other.  Thus,  if  A  museum  be  a  collection  of  speci- 
mens, then  A  scientific  museum  is  a  system^atized 
collection  of  specimens. 

§  81.  Infinitation.  This  mode  of  immediate 
inference  passes  from  the  purely  negative  to  the 
infinite  judgment  (§  53).  It  places  the  subject  in 
the  outer,  infinite  sphere.  Thus,  if  The  soul  he  not 
mortal,  then  The  soul  is  nonr-mortal.  These  prop- 
ositions express  different  thoughts.  They  are  sim- 
ilar, but  not  identical.  The  reverse  inference  is  in- 
cluded, for  the  sake  of  brevity,  under  the  same 
name.  Also  purely  affirmative  and  doubly  nega- 
tive propositions  are  infinitated ;  thus,  if  Man  he 
mortal,  then  No  man  is  non -mortal,  and  reversed. 
Hence  the  general  Rule  :  Change  the  quality 
of  the  judgment,  and  also  of  its  predicate. 
The  quantity  of  the  judgment  remains  unchanged. 
In  using  privatives,  as  in-,  un-,  dis-,  -less,  etc.,  we 
must  be  on  our  guard  lest  we  derive  too  much. 
With  this  precaution,  we  add  the  following  com- 
plete series  of  examples : 

Since  All  metals  are  fusible,      then   No  metal  is  infusible A  yields  E 

"     No  miser  is  happy,  "     Every  miser  is  unhappy . .  E      "     A 

•                 J       Ki      «  i  Some  sins  are  not  un-  )        t       «     ^ 
"     Some  sms  are  pardonable,   "  ■<            .      , ,  j.  . .  .  I       "     O 

(      pardonable ) 

"     Some  men  are  not  gentle,  "     Some  men  are  ungentle.  ..O      "     I 

§  82.  Conversion.  In  immediate  inference  by 
conversion,  the  terms  are  transposed.  Besides  ob- 
serving the  general  rules  already  given  (§§  75,  79), 


92  DEDUCTION 

we  must  take  heed  to  make  a  total  transference ; 
that  is,  the  whole  naked  subject  must  be  made 
predicate,  and  vice  versa.  By  naked  is  meant  with- 
out the  sign  of  quantity  all  or  some.  Thus,  from 
Every  old  man  has  heen  a  hoy.,  we  cannot  infer  that 
Some  hoy  has  heen  an  old  man.,  but  that  Some  one 
who  has  heen  a  hoy  is  an  old  man.  Hence  it  is  gen- 
erally needful  before  converting  to  reduce  the  prop- 
osition to  its  strict  logical  form. 

We  shall  consider  only  three  kinds  of  illative 
conversion,  and  these  only  so  far  as  our  subse- 
quent need  in  syllogizing  requires,  which  is  that 
we  be  able  to  convert  each  of  the  four  forms  A,  E, 
1,0. 

1st.  Simple  conversion  transposes  the  terms  with- 
out changing  the  quantity  or  the  quality  of  the 
proposition.     It  is  applied  to  E,  and  to  I ;  thus : 

No  one  without  sympathies  is  a  true  poet; E ana 

.'.No  true  poet  is  without  sympathies E 

Some  mathematicians  are  poor  financiers; I ifi 

/.Some  poor  financiers  are  mathematicians. ...  .1 

2d.  Conversion  per  accidens^  or  by  limitation,  j-e- 
duces  the  quantity  without  changing  the  quality 
of  the  proposition.  It  is  appUed  to  A,  and  the  con- 
verse is  I ;  thus  : 

All  plane  triangles  are  rectilinear  figures; A afl 

.'.Some  rectilinear  figures  are  plane  triangles I 

This  is  called  per  accidens  because  it  is  not  the 
transfer  of  a  predicate  per  se,  but  only  of  an  unes- 


IMMEDIATE   INFERENCE  93 

sential  or  accidental  part  which  that  term,  viewed 
universally,  includes. 

Observe  that  the  rule  in  §  79  forbids  retracing 
the  step,  reconverting  the  I  into  A,  which  would 
be  the  illicit  process. 

If,  on  subjecting  the  predicate  of  A  to  inquiry, 
the  proposition  is  recognized  as  afa,  as  when  a 
property,  a  definition,  or  a  division  is  predicated, 
then  it  is  convertible  simply. 

Also  E  may  be  converted  per  accidens  ;  but  this 
case  is  rather  simple  conversion  followed  by  subal- 
ternation. 

3d.  Conversion  hy  contraposition^  or  by  negation, 
changes  the  quality  but  not  the  quantity  of  the 
proposition.  It  is  applied  to  O,  and  the  converse 
is  I.  To  contrapone,  we  have  the  following  Rule  : 
Inflnitate,  and  then  convert  simply.     Thus : 

Some  pure  air  is  not  wholesome; O I ifi 

.•.Some  unwholesome  air  is  pure I 

This  is  evidently  a  double  process.  It  was  devised 
to  convert  O,  which  cannot  be  converted  simply  or 
per  accidens,  as  either  would  be  the  illicit  process. 
It  is  applicable  also  to  A. 

Upon  inspection  it  is  obvious  that  the  whole  doc- 
trine of  conversion  has  respect  to  extension.  An 
intensive  judgment  cannot  be  converted.  But  on 
changing  its  predicate  to  a  class  notion  it  becomes 
extensive,  and  so  convertible. 

Since  an  individual  cannot  be  a  predicate  (§  54), 


94  DEDUCTION 

it  follows  .that  an  individual  proposition  (§  63), 
though  it  be  symbolized  by  A  or  E  (§  67),  is  in- 
convertible. We  say  Juno  is  a  queen,  and  may  say 
One  queen  is  Juno  ;  but  this  apparent  conversion 
per  accidens  is  merely  a  rhetorical  inversion  (§  61) ; 
the  subject  of  thought  is  still  Juno.  No  mere  in- 
version is  a  logical  conversion. 

§  83.  Opposition.  A  proposition  in  any  one  of 
the  four  forms  A,  E,  I,  O,  is  in  opposition  to  the 
same  matter  in  each  of  the  other  three  forms.  The 
relations  are  such  that  if  the  given  proposition  be 
formally  true  or  false,  we  can  immediately  infer 
the  formal  truth  or  falsity  of  some  of  the  others. 
Opposition  is  of  four  kinds,  exhibited  thus : 

All  Salt  is  Pure,      A^ Contrary E     No  Salt  is  Pure. 

Square  of       ^  a  <^  "^        Opposition. 

Some  Salt  is  Pure,    I  Suhcontrary Q  Some   Salt   is    not 

Pure. 

1st.  Contradictory  opposition  exists  between  A 
and  O,  and  between  E  and  I,  propositions  having 
the  same  naked  or  unquantified  subject  and  predi- 
cate, but  which  differ  in  both  quantit}'  and  quality. 
EuLE :  Both  cannot  be  true,  and  both  cannot 
be  false.  This  is  merely  a  specific  statement  of 
the  Laws  of  Contradiction  and  Excluded  Middle 
(§  11).    E,  g..  If  All  Salt  is  Pure  be  sublated,  then 


IMMEDIATE    INFERENCE  95 

by  an  immediate  inference  we  can  posit  Some  Salt 
is  not  Pure.  If  Some  Salt  is  Pure  be  posited,  then 
we  can  immediately  sublate  No  Salt  is  Pure,  and 
so  on.  If  it  be  true  that  Every  man  has  a  con- 
science, then  it  cannot  be  that  Some  men  have  no 
conscience.  Such  propositions  are  said  to  be  dia- 
metrically opposed.  Contradiction  is  pre-eminently 
logical  opposition.  Also  it  is  complete ;  the  other 
forms  are  more  or  less  incomplete. 

2d.  Contrary  opposition  exists  between  A  and  E, 
universal  propositions  differing  in  quality  only. 
Rule  :  Both  cannot  be  true,  but  both  may  be 
false.  Between  A  and  E  there  is  a  tertium  quid, 
namely  I  and  O  (§  31).  If  All  S  is  P  be  posited, 
No  S  is  P  is  sublated,  and  vice  versa.  But  to  deny 
that  All  Stars  are  Planets  does  not  afford  the  in- 
ference that  No  Sta7's  are  Planets,  for  both  are  false, 
since  some  are,  and  some  are  not,  I  and  O. 

Contrariety  is  less  logical  than  metaphysical. 
Contradiction  occurs  only  in  thoughts,  and  contra- 
dictory thoughts  cannot  coexist.  It  cannot  occur 
in  things,  i.  e.  among  real,  external  objects,  contra- 
diction has  no  place.  Contrary  thoughts  can  co- 
exist— indeed  always  do  so — as  white  and  Uack, 
straight  and  crooked,  motion  up  and  down.  But 
these  cannot  coexist  in  reality,  in  external  things. 
Hence  contradiction  is  logical,  contrariety  physical, 
opposition.  Says  Aristotle :  Body  cannot  receive 
contraries  ;  mind  can  receive  contraries ;  therefore 
mind  is  not  corporeal. 

3d.  Suhcontrary  opposition  exists  between  I  and 


96  DEDUCTION 

O,  particular  propositions  differing  in  quality  only. 
Rule  :  Both  may  be  true,  but  both  cannot  be 
false.  They  are  compossible.  If  Scmie  S  is  P  he 
allowed  as  true,  it  may  be  that  Some  S  is  not  P  is 
also  true.  But  if  I  is  false,  then  O  must  be  true, 
and  mc6  versa.  We  remark,  how#Mer,  that  the 
some  in  the  two  propositions  must  be  a  different 
8om,e.  If  the  same  some  is  thought,  the  proposi- 
tions are  incompossible.  Also  that  if  the  scyme  is 
semi-definite,  the  rule  becomes :  Both  must  be  true. 
4th.  Subalternate  opposition  exists  between  A 
and  I  and  between  E  and  O,  propositions  differing 
in  quantity  only.  Eule:  If  the  universal  be 
true,  the  particular  is  true  ;  if  the  particular 
be  false,  the  universal  is  false.  This  is  not 
strictly  opposition,  but  rather  a  specific  application 
of  the  Law  of  Identity  (§  8).  No  illustration  is 
needed. 

These  formal  relations  arising  from  opposition 
may  be  tabulated  thus  : 

Contradictories.      Contraries.      Subalterns. 

(If  A  is  true,  O  is  false, E  false,  —  I  true. 
If  E  is  true,  I  is  false A  false O  true. 
If  A  IS  false,  O  is  true.  |  ,„,       ^,  ■,  ^       .      , 

If  E  is  false,  I  is  true,  f  ^he  others  undetermined. 

r  If  I  is  true,  E  is  false.  )  ^j^^  ^^^^^^  undetermined. 

Particulars     J   ?  ?^  f"^'  ^  ^'  !^^''-  ^     n  * 

If  I  IS  false,  E  is  true, O  true, A  false. 

I  If  O  is  false,  A  is  true, I  true, E  false. 

Hence  by  the  truth  of  universals,  and  by  the  falsity 
of  particulars,  all  others  are  determined ;  otherwise 
only  the  contradictory. 


y 


»  IMMEDIATE   INFERENCE  97 

Let  it  be  observed  that  when  the  proposition  is 
individual  (§  63)  all  the  distinctions  in  opposition 
are  merged  in  the  simple  negative,  which  is  com- 
plete contradiction ;  as,  Caliban  is  a  man,  and  Cali- 
ban is  not  a  man. 

§  84.  Praxis.  Draw  an  immediate  inference 
from  each  of  the  following  propositions : 

Infer  by  determination  from  the  three  following : 

1.  War  is  an  evil,    (Use  unprovoked,  and  welcomed  with 

ardor.) 

2.  The  ignorant  are  ceremonious.     (Use  an  age,  and 

a  nation.) 

3.  Honesty  deserves  reward.      (Combine  this  with :) 

Every  man  whom  we  meet  is  a  neighbor. 

Infinitate  each  of  the  following  propositions : 

4.  Some  men's  hearts  are  not  in  the  right  place. 

5.  It  is  wrong  not  to  reward  the  deserving. 

6.  In  jewels  and  gold,  men  never  grow  old. 

7.  There  are  studies  much  vaunted,  yet  of  little  utility. 

Convert  each  of  the  following,  and  affix  the 
symbols  as  in  §  82 : 

■'  >f  8.  None  are  free  wb«  do  not  govern  themselves. 

9.  With  man  many  things  are  impossible. 

10.  Whoso  loveth  instruction,  loveth  knowledge. 

,{,11.  Fair  promises  are  often  not  to  be  trusted. 

Contrapone  and  then  infinitate  the  following : 

'''^.2.  Seme  invisible  things  are  not  intangible. 
^'l3.  Every  unjust  action  is  inexpedient. 
7 


98  DEDUCTION 

If  the  following  be  true,  what  opposites  are  true, 
and  what  false  'i 

14.  By  night  an  atheist  half  believes  a  God. 

15.  No  one  is  always  happy. 

16.  Some  democracies  are  unstable. 

17.  Some  great  orators  are  not  statesmen. 

If  the  following  be  false,  what   opposites  are 
false,  and  what  true  ? 

18.  All  self-confident  persons  have  strong  will. 

19.  No  honest  men  become  bankrupt. 
//y  20.  Some  private  vices  are  public  benefits. 

'    21.  Some  plants  do  not  produce  seed. 


-< 


k-/a_a_^^ -ir— <5    <^      V,     'vc     _    pJ 


II.— THE   SYLLOGISM 

§  85.  When  we  are  unable  to  judge  directly  the 
relation  of  two  given  notions,  resort  is  had  to  some 
third  notion  as  a  medium,  which,  being  directly 
compared  with  each  of  the  former,  enables  us  to 
see  their  agreement  or  disagreement,  and  conse- 
quently to  conjoin  or  disjoin  them.  This  is  medi- 
ate inference  or  reasoning  (§  77).  For  example, 
take  the  notion  man^  and  the  VLoWoxi  fre^-willed.  On 
comparing  these,  we  are  unable,  perhaps,  to  judge 
whether  or  not  this  mark  belongs  to  that  concept. 
So  we  seek  a  medium  of  comparison.  We  find  the 
notion  responsible^  and  see  directly  that  Tnan  in- 
volves responsible^  likewise  that  responsible  com- 
prehends/Vee  /  thus  we  come  to  see  that  man 
involves  yV^.  This  is  the  intensive  view.  It  is 
formally  stated  thus :  v^ 

Every  maiwis  respojuible ; 
Every  responsit^le  is^^ee; 
.".Every  man  is  free. 

Again,  we  are  unable  to  judge,  perhaps,  whether  or 
not  man  is  contained  under  the  class  free  agent. 
But  we  judge  that  man  is  contained  under  the  class 
responsible  agent,  and  this  under  the  classyV^e  agent, 
and  so  conclude  man  to  be  d,  free  agent.  This  is 
the  extensive  view.     It  is  formally  stated  thus : 


it 

100  ^         DEDUCTION 

Every  responsible  agent  is  a  free  agent ; 
Every  man  is  a  responsible  agent ; 
.'.  Every  man  is  a  free  agent. 

A  mediate  judgment  thus  formally  and  fully  ex- 
pressed is  called  a  syllogism.  What  is  subjectively 
a  reasoning  is  objectively  a  syllogism.  Hence  the 
definition :  A  syllogisni_is_a_  reasoning  fullyL_and 
regularly  expressed  in  language.  What  is  meant 
by  regularly  will  more  clearly  appear  hereafter. 
Another  definition  is :  A  syllogism  is  an  inference 
by  which  a  proposition  is  derived  from  two  others 
conjointly,  the  one  being  virtually  contained  in  the 
others 

§  86.  In  dissecting  the  syllogism  we  find  three 
propositions,  two  antecedents  or  premises,  and  a 
consequent  or  conclusion.  To  conclude  is  to  shut 
up  together  in  the  last  proposition  notions  which 
stood  apart  in  the  first  two.  The  word  syllogism 
also  means  a  collecting  together.  The  following  is 
an  example  in  extension : 


All  Men  are  Persons;  =M 
All  Slaves  are  Men ;  =  S 
'.All  Slaves  are  Persons;  =  S 


—  P  =  Major  Premise; 

—  M=  Minor  Premise; 

—  P  =  Ck>nclusion. 


Here  are  only  three  notions  or  terms,  Sla/ves, 
Men,  Persons.  These  are  in  the  relation  of  whole 
and  part.  Slaves  being  contained  under  Men,  and 
Men  under  Persons.  P,  then,  is  the  term  of  wid- 
est extent  (as  in  the  notations),  or  the  Major  Term ; 
Sot  least  extent,  or  the  Minor  Term ;  and  M,  in  this 


THE   SYLLOGISM  101 

case,  of  intermediate  extent,  or  the  Middle  Term. 
The  latter  occurs  in  each  of  the  premises,  but  not 
in  the  conclusion.  The  two  former,  called  the  Ex- 
tremes, constitute  the  conclusion.  We  may  now 
define  as  follows : 

The  Middle  Term  (M)  is  the  one  with  which 
each  of  the  extremes  is  compared  in  the  premises. 
It  is  also  called  the  Argument,  or  the  Reason. 

The  Major  Term  (P)  is  the  extreme  of  greater 
quantity,  or  the  greater  whole.  It  is  always  (in 
extension)  the  Predicate  of  the  conclusion. 

The  Minor  Term.  (S)  is  the  extreme  of  less 
quantity,  or  the  lesser  whole.  It  is  always  (in  ex- 
tension) the  Subject  of  the  conclusion. 

The  Major  Premise  is  the  premise  containing 
the  Major  Term.  It  is  usually  placed  first.  It  is 
also  called  the  Sumption. 

The  Minor  Premise  is  the  premise  containing 
the  Minor  Term.  It  is  usually  placed  second.  It 
is  also  called  the  Subsumption. 

Observe  that  the  middle  term  is  not  so  called 
because  of  intermediate  extent,  but  because  it  is 
the  medium  of  comparison.  There  are  many  cases 
in  which  it  has  not  intermediate  extent. 

The  order  of  the  propositions,  the  major  premise 
first,  the  minor  second,  and  the  conclusion  last,  is 
arbitrary,  and  merely  agreed  upon  for  the  sake  of 
uniformity.  Also  that  there  are  three  distinct 
propositions.  It  is  easy  and  accurate  to  state  the 
reasoning  in  an  inverted  order,  and  in  a  single 
proposition ;  as.  That  slaves  are  persons  is  an  infer- 


102  DEDUCTION 

encefrom  the  judgments  that  they  are  men,  and  that 
men  are  persons. 

In  the  foregoing  example  all  the  propositions  are 
universal  and  affirmative.  The  following  differs  in 
these  respects ; 

No  murmurs  are  prayers. ,  .(E)   /^     ^        ^^     ^        Prayers. 

p      \         Murmurs. 


^{ 


Some  sighs  are  murmurs ...  (I)  \        j^"^  V        J      P'^^^- 

V         y  x»-h:M— ,S 

.'.  Some  sighs  are  not  prayers .  (O)  V /  | 

In  this  example  one  premise  is  particular,  and  one 
negative,  yielding  a  conclusion  which  is  both. 

§  87.  Let  us  consider  the  several  notations.  The 
circular  and  linear  have  already  been  mentioned 
(§  25),  and  on  slight  inspection  are  easily  under- 
stood. The  circular  is  objectionable,  as  allowing  a 
great  variety  of  insignificant  arrangement,  and  also 
as  constantly  signifying  too  much.  For  instance, 
in  the  last  example  it  expresses  No  S  is  P,  and 
also  that  Some  S  is  not  M,  or  the  semi -definite 
some.  The  linear  has  the  advantage  that  only 
those  parts  of  the  lines  opposite  each  other  are 
compared.  Of  what  is  beyond  the  limit  of  com- 
parison nothing  is  said,  the  extension  of  the  line 
merely  serving  to  show  that  it  is  indefinite.  For 
this  and  other  reasons  the  linear  is  preferable  to 
the  circular. 

These  notations  are  not  at  all  applicable  to  in- 
tension, but  only  to  extension.  But  even  as  ap- 
plied to  extension  they  are  radically  objectionable. 


THE   SYLLOGISM  103 

Both  circles  and  lines  have  geometrical  extension 
only,  and  are  quantities ;  and  therefore  when  used 
to  figure  qualitative  notions  they  transfer  thought 
to  the  quantitative  or  mathematical  whole  (§  23), 
and  so  induce  confusion.  This  is  favored  by  the 
ambiguity  of  the  word  extension,  and  has  doubt- 
less been  influential  in  promoting  the  unnatural 
and  false  view  that  all  propositions  are  equations, 
and  logic  a  branch  of  applied  mathematics  (§  Y4). 
The  circular  and  linear  notations  are  therefore  cov- 
ertly false  and  misleading.  We  shall  not,  however, 
wholly  discard  them,  for  by  long  and  widely  ap- 
proved usage  they  have  become  almost  an  integral 
part  of  elementary  logic;  but  we  caution  the 
reader  by  pointing  out  their  essentially  erroneous 
representation. 

Another  mode  of  notation,  called  graphic  nota- 
tion, is  shown  in  connection  with  the  examples. 
It  needs  some  explanation.  A  colon  standing  next 
a  term  indicates  that  it  is  distributed ;  a  comma, 
that  it  is  undistributed.  The  positive  copula  is  ex- 
pressed by  a  pointed  dash  (  — ),  in  manuscript  a 
slight  pen-stroke ;  the  negative  by  the  same  crossed 
(  H-).  A  peculiar  advantage  of  this  device  is  that  it 
discriminately  expresses  either  extension  or  inten- 
sion. Pointing  to  the  predicate,  the  copula  indi- 
cates an  extensive  judgment ;  thus  M  :  -^  P  reads 
All  M  is  (contained  under)  P ;  P  -h  :  M  reads  No 
M  is  (contained  under)  P ;  M  —  ,  S  reads  Some  S 
is  (contained  under)  M.  The  long  dash  is  the 
copula  of  the  conclusion ;  thus,  P  — ^—-  ,  S  reads 


104  DEDUCTION 

Some  S  is  not  (contained  under)  P.  Pointing  to 
the  subject,  the  copula  indicates  an  intensive  judg- 
ment ;  thus  S  :  ^  M  reads  All  S  is  (comprehends) 
M ;  S  , <r^—  P  reads  Some  S  is  not  (does  not  com- 
prehend) P.  When  needful,  a  sign  of  quantifica- 
tion ( ,  or  : )  may  be  added  to  the  predicate  also. 
This  admirable  method  of  notation  is  very  elastic, 
capable  of  expressing  thought  relations  accurately, 
and  is  recommended  for  constant  use. 

§  88.  In  the  intensive  syllogism  the  predicates 
are  marks.  The  following  is  an  example,  with  its 
graphic  notation : 


Silver  is  Metallic ;  =  S 

In  Intension  ■{      Metal  is  Positive ;  =  M 

.  Silver  is  Positive.   =  S 


-MJ 

^p  1  =  8:  — M:  —  ] 


By  positive  is  meant  electro-positive.  The  same 
matter  transformed  yields : 

iAU  Metals  are  Positive  elements;  J 
Silver  is  a  Metal ;  >-=P  — :M— :S 

.*.  Silver  ia  a  Positive  element.  )  ^^~~ 

Here  the  relative  quantity  of  the  extremes  is  in- 
verted ;  the  greater  part  in  extension,  P,  is  the  less- 
er part  in  intension,  and  vice  versa  (§  54).  This  is 
in  accord  with  the  law  that  extension  and  inten- 
sion are  in  inverse  ratio  (§  20).  In  the  example, 
Silver  comprehends  Metallic,  and  this  comprehends 
Positive ;  S  is  obviously  the  greatest  whole,  and  P 
the  least.  Hence,  in  intension  the  major  term  is 
the  subject  of  the  conclusion,  and  the  minor  term 


THE    SYLLOGISM  '  105 

its  predicate.  And,  since  it  is  agreed  to  place  the 
major  premise  first,  the  order  of  the  premises  is 
transposed.  Consequently,  for  changing  either  form 
into  the  other,  we  have  the  following  Rule: 
Transpose  the  premises,  and  invert  the 
copulas;  that  is,  instead  of  comprehends^  read  ia 
contained  under ^  and  vice  versa. 

§  89.  The  distinction  between  the  extensive  and 
intensive  syllogism  has  been  discussed  because  need- 
ful in  order  to  general  definition,  and  to  a  complete 
view  of  the  dissected  parts.  "We  are  now  prepared 
to  make  an  estimate,  briefly  and  once  for  all,  of  the 
value  of  the  distinction.  The  grammatical  differ- 
ence, which  frequently  but  not  always  appears,  be- 
tween substantive  and  adjective  noun  forms  in  the 
predicate  is  hardly  a  logical  difference.  This  apart, 
the  external  difference  lies  wholly  in  transposed 
premises.  But  the  order  of  the  premises  being 
merely  conventional,  any  distinction  founded  there- 
on is  arbitrary  and  artificial,  not  real  and  natural, 
and  so  goes  for  nothing.  The  other  difference 
named  in  the  rule  is  the  inversion  of  the  copulas. 
This  is  not  an  external  difference.  Ordinarily  the 
copula  is  wholly  indifferent  and  ambiguous,  and  its 
special  meaning  is  indicated  only  by  unusual  sub- 
stitutions (§  54). 

The  difference,  then,  lies  entirely  in  the  thought, 
in  the  modes  extension  and  intension,  and  the  con- 
sequently reversed  relation  of  part  and  whole.  That 
this  is  a  difference  in  kind  may  be  granted,  one  to 


106  DEDUCTION 

be  noted  in  an  exposition  of  mental  modes,  and  in 
a  theory  of  thought.  But  it  is  of  very  small  log- 
ical consequence.  Both  forms  of  the  syllogism  are 
mediate  inferences  through  the  same  medium ;  both 
reach  the  same  conclusion ;  the  formal  expression  of 
both  is  the  same ;  the  supreme  canon  (§  93)  is  essen- 
tially the  same  for  both  ;  the  general  rules  (§  94)  are 
the  same ;  and  the  special  rules  (§  97)  need  for  ad- 
aptation only  the  interchange  of  the  words  major 
and  minor;  hence  no  general  modification  of  the 
old  logical  doctrine  is  called  for  by  introducing  the 
intensive  syllogism. 

The  practical  difference  is  of  no  moment.  When 
we  consider  that  one  of  these  modes  subjectively, 
and  with  the  greatest  facility,  changes  to  the  other, 
and  that  without  further  consequence,  we  ask: 
What  is  the  worth  of  a  difference  between  forms 
so  completely  and  readily  transmutable  ?  The  two 
always  actually  coexist  in  thought  as  psychological 
correlatives,  one  more  obscure  than  the  other  (§  20), 
and  their  convertibility  would  indicate  rather  iden- 
tity, being  inconsistent  with  the  opposition  which 
belongs  to  kinds.  Moreover,  we  very  often  use 
both  forms  in  one  reasoning.     For  example  : 

All  of  the  metals  are  positive; Intensive. 

Silver  is  one  of  the  metals; Extensive. 

.'.Silver  is  positive Intensive. 

This  is  formally  perfect,  calling  for  no  logical  mod- 
ification whatever. 
From  these  considerations  we  conclude  that  it  is 


THE   SYLLOGISM  107 

needless  to  continue  to  observe  the  distinction.  Let 
the  reader,  then,  understand  that  hereafter  we  shall 
view  all  matter  primarily  in  the  form  of  extension, 
even  when  adjective  predicates  are  used,  satisfied 
that  at  any  instant  the  view  can  readily  be  re- 
versed, and  noting  expressly  the  form  of  intension 
only  in  special  cases. 

§  90.  Formally  stated,  a  syllogism  consists  of 
three  propositions.  But  let  it  not  be  understood 
that  a  syllogistic  judgment  or  reasoning  consists  of 
three  judgments.  Two  judgments  are  premised ; 
then  parts  of  these  are  combined.  This  last  alone 
is  the  act  of  mediate  comparison,  the  syllogistic 
judgment,  the  reasoning;  and  it  is  a  single  act  of 
mind,  a  single  thought,  only  one  judgment.  Sub- 
sequently it  is  formally  stated  as  a  third  proposi- 
tion, the  conclusion. 

In  the  definition  of  inference  it  is  said  that  some- 
thing distinct  from  what  is  laid  down  follows  of 
necessity  (§  T7).  Accordingly,  the  essence  of  the 
syllogism  is  the  necessary  sequence  of  the  conclu- 
sion from  the  premises.  This  necessity  flows  from 
the  necessary  character  of  the  Primary  Laws 
(§§  ^5  ^\  to  which  the  syllogism  conforms,  and  by 
which  alone  it  is  ultimately  governed.  It  is  some- 
times expressed  in  the  conclusion  by  the  addition 
of  must.     For  example : 

If  all  metals  are  fmsible, 
And  gold  is  a  metal, 
Gold  must  be  fusible. 


108  DEDUCTION 

The  common  distinction,  then,  between  demon- 
strative and  moral  or  probable  reasoning  lies 
wholly  in  the  matter,  not  at  all  in  the  form.  The 
form  is  in  all  cases  demonstrative,  apodeictic,  nec- 
essary. 

§  91.  Since  logic  is  not  at  all  concerned  with  the 
matter  of  thought  (§  50),  it  has  no  regard  for  the 
material  truth  or  falsity  of  syllogistic  propositions, 
but  only  for  the  relation  of  sequence.  In  view  of 
this  fact,  it  would  be  an  improvement  if  the  prem- 
ises in  logical  examples  of  the  syllogism  were  ex- 
pressed not  categorically,  but  conditionally,  as  in 
the  example  in  the  preceding  section.  The  mind 
of  the  reader  would  then  be  less  drawn  to  the  truth 
or  falsity  of  the  propositions,  which  is  not  at  all  in 
question,  and  away  from  the  form,  which  is  the 
sole  consideration.  For  the  same  reason,  illustra- 
tions whose  matter  is  trite  and  familiar  are  to  be 
preferred. 

But  some  remark  upon  the  relations  of  the  parts 
of  the  syllogism  with  reference  to  formal  truth 
and  falsity  is  desirable.  The  antecedents  being 
granted,  the  consequent  must  also  be  allowed.  If^ 
the„anlficedents  be  true,  necessarily  the  consequent 
is  true.  Whatever  measure  of  doubt  attaches  to 
tHe^ntecedents,  just  that  degree  of  uncertainty — 
no  more,  no  less — belongs  to  the  consequent.  Should 
^e  antecedents  be  false,  it  does  not  follow  thaT^ 
the  consequent  is  false ;  it  is  merely  unproven,  and 
may,  perhaps,  be  established  by  other  antecedents. 


THE    SYLLOGISM  109 

These  antecedents,  being  false,  prove  nothing : 

The  natives  of  Italy  were  Greeks  ; 
The  Athenians  were  natives  of  Italy; 
/.The  Athenians  were  Greeks. 

This  example  shows  also  that  the  truth  of  the  con- 
sequent does  not  guarantee  that  of  the  antece- 
dents. But  if  the  consequent  be  false,  it  follows 
that  at  least  one  of  the  antecedents  is  false.  These 
points  may  be  summarized  thus : 

Affirming  the  antecedents,  affirms  the  conse- 
quent. 

Denying  an  antecedent,  nothing  follows. 

Affirming  the  consequent,  nothing  follows. 

Denyingjhe  consequent,  denies  an  antecedent. 

§  92.  Praxis.  Point  out  the  major,  minor,  and 
middle  terms  in  the  following  reasonings,  and  re- 
dress them  in  syllogistic  order.  Then  write  the 
circular,  linear,  and  graphic  notation  of  each : 

1.  True  poets  are  men  of  genius ;  but  since  very  un- 

wise men  sometimes  prove  true  poets,  they  must 
be  men  of  genius, 

2.  Whatever  is  universally  believed  must  be  true.     This 

may  be  said  of  the  existence  of  God,  which,  there- 
fore, must  be  a  truth. 

3.  No  duty  involves  loss ;  hence  to  give  freely  does 

not  always  involve  loss,  for  this  is  occasionally  a 
duty. 

4.  Sensualists  are  not  free ;  for  they  are  governed  by 

passion,  and  no  one  so  governed  is  free. 

Write  the  graphic  notation  of  each  of  the  fol- 


110  DEDUCTION 

lowing  syllogisms,  then  change  the  extensive  to  the 
intensive  form,  and  vice  versa,  and  write  the  graphic 
notation  of  the  result : 

5.  All  men  are  liable  to  err ; 

None  liable  to  err  are  safe  from  disaster ; 
/.  No  man  is  safe  from  disaster. 

6.  All  expedient  actions  are  justifiable  actions ; 
Some  wars  are  expedient  actions ; 

/.  Some  wars  are  justifiable  actions. 

Answer  the  questions  appended  to  the  following 
syllogism : 

7.  If  infants  have  no  language,  and  if  they  reason,  then 

some  reasoning  is  possible  without  language. 
But  the  sumption  is  quite  doubtful ;  therefore,  what 

follows  ? 
But  the  subsumption  is  not  true ;   therefore,  what 

follows  ? 
But   the   conclusion   is   not  true ;    therefore,  what 

follows  ? 
But  the  conclusion  surely  is  true ;  therefore,  what 

follows  ? 
But  both  of  the  premises  are  true ;  therefore,  what 

follows  ? 


III.— CANON  AND  RULES 

§  93.  The  syllogistic  judgment  that  the  antece- 
dents necessitate  the  consequent  (§  90)  is  deter- 
mined by  the  Primary  Laws.  Since  these,  howev- 
er, because  of  their  wide  generality,  are  not  readily 
applicable,  the  principle  of  the  syllogism  is  ex- 
pressed in  a  single  special  Canon  which  can  be  used 
as  a  direct  test  of  its  validity.  We  select  four  out 
of  many  modes  of  statement. 

1.  Part  of  a  part  is  part  of  the  "whole.  As 
marks  are  parts  of  a  notion,  and  species  parts  of  a 
genus,  this  is  obviously  applicable  to  both  exten- 
sion and  intension  in  the  qualitative  whole.  Also, 
it  applies  to  the  quantitative  whole.  Its  general- 
ity, brevity,  and  simplicity  render  it  very  useful. 
It  is,  however,  inadequate,  being  applicable  only 
to  affirmative  syllogisms.  A  modified  formula, 
limited  to  the  qualitative  whole,  is :  What  is  said 
distrihutively  of  a  whole  may  he  said  of  a  part. 

Let  the  reader  apply  these  formulas  to  any  of 
the  foregoing  affirmative  syllogisms,  and  the  mean- 
ing will  become  clear. 

2.  Quicquid  de  omni  valet,  valet  etiam  de  quibus- 
dam  et  singulis.  Quicquid  de  nullo  valet,  nee  de 
quihusdam  nee  de  singulis  valet.     These  are  the 


112  DEDUCTION 

famous  Dicta  de  omni  et  nullo  of  the  schoolmen. 
They  have  been  often  and  sharply  criticised  as 
senseless,  the  first  being  charged  with  saying 
merely  Whatever  is  true  of  each^  is  true  of  each',  the 
second,  What  is  not  true  of  any,  is  not  true  of  any. 

3.  Whatever  is  discovered  or  admitted  as 
predicable  distributively  of  a  class,  must  be 
allowed  as  predicable  of  any  of  its  discovered 
or  admitted  m.em.bers. 

This  formula,  carefully  worded  to  avoid  similar 
reproach,  is  applicable  to  syllogisms  both  positive 
and  negative,  but  is  limited  in  expression  to  those 
in  extension.  We  note  :  predicahle,  positively  or 
negatively;  discovered,  by  intuition,  by  induction, 
or  by  testimony ;  admitted,  by  hypothesis,  or  mere- 
ly for  sake  of  argument ;  of  a  class,  as  an  undivided 
whole ;  must,  necessity ;  members,  species  or  indi- 
viduals. 

4.  Any  notion  may  be  replaced  by  its  equiv- 
alent ;  or  by  its  undistributed  genus ;  or,  if 
distributed,  by  any  of  its  parts. 

This  canon  of  replacement  is  here  proposed  as 
more  general  than  the  others,  and  as  more  truly 
expressive  of  the  actual  process  of  thought.  It  is 
simple  and  self-evident.  The  first  clause  is  appli- 
cable to  coextensive,  or  equipollent,  or  mathemati- 
cal equivalence.     For  instance : 

A  is  equal  to  B  ; 
B  is  equal  to  C  ; 
.'.A  is  equal  to  C.  .(replacing  the  first  B  by  its  equivalent  (J). 

The  several  clauses  are  applicable  to  the  various 


CANON   AND   KULES  113 

forms  of  immediate  inference.  For  instance,  con- 
version per  acddens  may  be  viewed  thus : 

All  men  are  men ; (mere  identity). 

Prop.  .All  men  are  mortals  ; {mortals,  genus  of  men). 

/.Some  mortals  are  men.  .(replacing  the  first  all  men 
by  its  undistributed  genus). 

The  view  taken  in  this  canon  of  the  qualitative 
syllogism  is  peculiar.  It  considers  the  sumption 
as  stating  a  relation  between  two  notions;  the 
subsumption  as  stating  that  some  other  notion  is  a 
part  of  one  of  them ;  the  syllogistic  judgment  as 
replacing  that  one  by  this  part ;  and  the  conclusion 
as  setting  forth  the  result.     For  instaiice : 

All  men  are  mortal ; (sumption). 

Socrates  is  a  man  ; (he  is  one,  a  part  of  all  men"). 

.'.  Socrates  is  mortal (replacing  all  men  by  this  part). 

The  third  clause  of  the  canon  applies  thus  to  syllo- 
gisms of  the  first  and  second  figure;  the  second 
clause,  to  those  of  the  third  figure.  Moreover,  some 
natural  and  very  simple  forms  of  reasoning,  which 
it  is  difficult  to  put  in  strict  logical  form,  are  directly 
justified  by  this  canon.  For  instance,  the  follow- 
ing has  been  accounted  a  sore  logical  puzzle : 

The  divine  law  commands  us  to  honor  kings  ; 
Louis  XIV.  is  a  king  ; 
.'.  The  divine  law  commands  us  to  honor  Louis  XIV. 

Its  solution  by  replacement  is  easy.  In  the  sump- 
tion kin§s  is  a  distributed  notion,  and  in  the  con- 
clusion is  simply  replaced  by  its  part,  Louis  XIV. 
This  seems  to  be  the  actual  mental  process  by 
which  a  ckild  would  accept  this  conclusion. 


1 14  DEDUCTION 

§  94.  The  canon  in  its  original  and  usual  form 
is  directly  applicable  only  to  syllogisms  of  the  first 
figure.  For  this  reason,  and  because  its  use  as  a 
test  is,  in  some  cases,  rather  confusing,  logicians 
have  resolved  its  principle  into  a  series  of  distinct 
General  Rules  applicable  to  any  figure.  All 
sound  reasoning  must  conform  to  these  rules.  Be- 
ing quite  simple  and  used  separately,  they  render 
the  process  of  testing  a  syllogism  easy,  quick,  and 
sure.     They  are  as  follows  : 

1.  A  syllogism  has  three,  and  only  three, 
terms.  For  a  reasoning,  which  it  expresses,  com- 
prises three,  and  only  three,  notions — two  compared 
by  means  of  a  third.  A  good  syllogism  is  a  tripod. 
The  following  is  a  quadruped  ;  verbally  it  is  a  triad, 
but  in  thought  quatemio  terminorum,  and  hence 
called  a  quaternion : 

Light  is  contrary  to  darkness  ; 

Feathers  are  light ; iJigM  equivocal). 

.*.  Feathers  are  contrary  to  darkness. 

2.  A  syllogism  has  three,  and  only  three, 
propositions.  For  three  terms  give  three  pairs, 
and  three  only.     Apparently  we  have  more  in — 

All  beings  that  have  nerves  are  sentient A 

All  self-moving  things  have  nerves A 

Worms  are  self-moviiig A 

.'.  "Worms  are  sentient A 

The  reasoning  is  good,  the  form  logical;  but  we 
shall  find  in  a  subsequent  analytical  study  (§  106) 
that  it  is  a  Sorites,  resolving  into  two  syllogisms 
of  three  propositions  each. 


CANON   AND    RULES  115 

3.  One  premise  at  least  must  be  affirmative. 

For  if  the  middle  term  agrees  with  neither  of  the 
other  two,  we  cannot  infer  through  it  whether  or 
not  they  agree  with  each  other.  From  the  follow- 
ing negative  premises — 

No  marble  is  sentient E 

Some  statues  are  not  marble O 

we  get  no  conclusion ;  for,  however  true  it  may 
be,  they  do  not  prove  some  statues  not  sentient. 
But  the  following  yield  a  conclusion : 

No  man  is  without  religious  feeling E 

Many  men  are  not  true  believers I 

.".  Many  infidels  are  not  without  religious  feeling O 

But  the  minor  premise  is  really  affirmative,  the 
negative  particle  belonging  to  the  predicate,  which 
thereby  becomes  equivalent  to  infidels,  and  consti- 
tutes the  subject  of  the  conclusion. 

4.  If  one  premise  be  negative,  the  conclu- 
sion must  be  negative.  For  if  one  extreme  be 
denied  to  the  middle  term,  it  must  be  denied  final- 
ly to  the  other  extreme  which  agrees  with  the 
middle  term  by  Rule  3.    For  example : 

Few  men  weep O 

All  men  feel A 

We  cannot  conclude  Some  who  feel  weep.  How- 
ever true  it  may  be,  these  premises  do  not  yield  it. 
Few  is  essentially  negative  (§  65),  and  gives  a  nega- 
tive sumption,  yielding  a  negative  conclusion  : 

Sumption, Most  men  do  not  weep O 

Now  subsume,  . . .  All  men  feel A 

Hence  conclude, .  .Many  who  feel  do  not  weep O 


116  DEDUCTION 

5.  The  middle  term  must  be  total  at  least 
once.  For  if  in  each  premise  it  is  used  in  a  partial 
sense,  it  may  in  each  denote  different  objects,  and 
so  be  equivalent  to  two  terms,  making  four  in  all, 
in  violation  of  Rule  1.     From  these  premises — 

Some  of  our  students  use  profane  language I 

Some  of  our  students  are  refined  gentlemen I 

we  can  conclude  nothing,  for  the  middle  evidently 
refers  to  entirely  different  groups.  This  is  the  fal- 
lacy of  undistributed  middle.  Sometimes  it  is  not 
quite  so  obvious  ;  for  example : 

A  valid  syllogism  has  three  terms A 

This  syllogism  has  three  terms A 

.*.  This  is  a  valid  syllogism A 

Here  the  middle  is  in  each  case  the  predicate  of  an 
affirmative,  and  is  not  distributed  (§  75),  and  so  the 
conclusion  is  unproven. 

If,  however,  an  undistributed  middle  be  so  quan- 
tified that  the  sum  of  its  portions  is  more  than  the 
whole,  a  conclusion  is  competent.  This  is  called 
the  Ultra-total  Quantification  of  the  Middle  Term — 

Two  thirds  of  mankind  are  Asiatics I  Asiatics 

Two  thirds  of  mankind  are  heathen I  I       mankind 

.'.  Some  heathen  are  Asiatics I  heathen"! 

(At  least  one  half  are,  perhaps  aW  are.)  1         ' 

The  early  logic  makes  no  mention  of  this  appar- 
ent exception  to  the  rule,  which  is  apparent  only, 
not  real,  for  the  reasoning  is  in  the  quantitative, 
rather  than  in  the  qualitative,  whole. 

6.  An  extreme,  if  partial  ia  a  premise, 
must  be  so  in  the  conclusiom.    For  if  only  some 


CANON   AND   KULES  117 

is  premised,  we  cannot  conclude  all ;  we  cannot 
argue  from  part  to  wliole.  The  violation  of  this 
rule  is  the  fallacy  of  illicit  process  (§  79).  It  is 
illicit  major  or  illicit  minor,  according  to  the  term 
to  which  the  fault  attq,ches.     For  example : 

All  birds  are  winged A 

A  bat  is  not  a  bird E 

.'.  A  bat  is  not  winged E 

Here  the  major  terra  winged  is  not  distributed 
(i.  e.  is  partial)  in  the  premise,  since  it  is  there  the 
predicate  of  an  affirmation ;  but  it  is  distributed 
(i.  e.  is  universal)  in  the  conclusion,  since  it  is  there 
the  predicate  of  a  negation.  Hence  there  is  an 
illicit  process  of  the  major  terra.  The  following  is 
an  illicit  process  of  the  minor  term : 

Persons  without  imagination  are  not  true  poets.. E 

Good  logicians  are  often  without  imagination I 

.*.  Good  logicians  are  not  true  poets E 

Illicit  major  occurs  only  when  the  conclusion  is 
negative.  Illicit  minor  occurs  only  when  the  con- 
clusion is  universal. 

7.  One  premise  at  least  must  be  universal. 
For  if  the  premises  be  I  I,  there  is  no  distributed 
term  for  a  middle  (Rule  5).  If  they  be  O  O,  both 
premises  are  negative  (Rule  3).  If  they  be  I  O  or 
O  I,  there  is  but  one  terra  distributed,  the  predi- 
cate of  O ;  if  this  be  taken  for  the  raiddle  terra, 
then  illicit  raajor,  since  the  negative  conclusion 
required  by  Rule  4  distributes  its  predicate,  the 
major  term ;  if  it  be  not  so  taken,  then  undistrib- 
uted middle  (Rule  5). 


118  DEDUCTION 

8.  If  one  premise  be  particular,  the  con- 
clusion must  be  so.    For  a  universal  following 

A  with  I  would  require  2  distributed  terms  ;  there  is   but  1  ; 
A    "    O      "  "        3  "  "  "      are  but  2; 

E     "     I      "  "3  "     .         "  "    .    "     "    2; 

E     "    O,  both  negative  (Rule  3).     No  conclusion  whatever. 

§  95.  Praxis.  Keduce  all  propositions  to  strict 
logical  form  (§  61),  and  arrange  them  in  syllogistic 
order  (§  86). 

Apply  the  first  canon,  pointing  out  the  parts 
and  whole,  to — 

1.  The  truly  virtuous  are  truly  happy.     The  poor  are 

often  the  one,  and  therefore  the  other. 

Apply  the  third  canon,  pointing  out  the  class 
and  its  member,  to — 

2.  All  planetary  bodies  move  in  elliptic  orbits  {hy  induc- 

tion).     Now,  if  an  asteroid  be  truly  a  planet  [hy 
hypothesis),  then  the  orbit  of  an  asteroid  is  elliptic. 

Apply  the  canon  of  replacement,  supplying  the 
conclusion,  to — 

3.  The  gospel  promises  salvation  to  the  faithful ;  yet 

many  are  faithful  whom  the  world  condemns. 

Affix  the  symbol  to  each  proposition,  and  then 
point  out  what  rule  or  rules,  if  any,  are  violated 
in  the  following  examples: 

4.  Many  who  conquer  their  passions  have  strong  will ; 
Whoever  resists  temptation  conquers  his  passions ; 

.•.  Whoever  does  not  yield  possesses  powerful  will. 


CANON    AND   RULES  119 

6.  No  sentient  being  is  without  a  nervous  system  ; 

The  sensitive  mimosa  is  not  sentient ; 
.-.  The  sensitive  mimosa  has  no  nervous  system. 

6.  Whatever  causes  intoxication  should  be  prohibited ; 
The  use  of  wine  causes  intoxication ; 

.'.  The  use  of  wine  should  be  prohibited. 

7.  No  one  is  rich  who  is  not  content ; 
No  miser  is  content ; 

/.  No  miser  is  rich. 

8.  Few  men  are  entirely  unworthy  of  respect ; 
Most  men  are  unlearned  ; 

.',  Some  unlearned  men  are  worthy  of  respect. 

9.  Some  a;  is  y  ;  every  y  is  not  z  ;  hence  some  x  is  not  z. 

10.  No  rose  is  without  thorns  ; 
This  bouquet  is  of  roses ; 

.'.  This  bouquet  has  thorns. 

11.  All  rational  beings  are  accountable  for  their  actions; 
But  many  that  suffer  punishment  are  irrational ; 

/.  Many  that  suffer  punishment  are  not  accountable  for 
their  actions. 

12.  Every  man  ha«  wants; 

All  men  are  rational  animals ;  .  .  .  afa 
/.  Every  ratL»nal  animal  has  wants. 

13.  All  householders  pay  taxes  ; 

The  voters  are  those  that  pay  taxes ;  .  .  afa 
.♦.  All  householders  are  voters. 

N.  B. — With  reference  to  the  forms  of  examples  12 
and  13,  see  §  146  and  §  131. 


IV.— FIGURE  AND  MOOD 

§  96.  Syllogisms  are  divided  into  Figures  accord- 
ing to  the  position  of  the  middle  term.  In  the 
First  Figure,  it  is  the  subject  of  the  major  premise, 
and  predicate  of  the  minor.  In  the  Second,  it  is 
predicate  of  both.  In  the  Third,  it  is  subject  of 
both.  In  the  Fourth,  it  is  predicate  of  the  major, 
and  subject  of  the  minor.     Thus : 

Fig.  1.  Fig.  2.  Fig.  3.  Fig.  4. 

M^P  P^M  M^P  P— M 

S  — M  S^M  M-S  M^S 

.-.S  -  P  .-.S  —  P  .-.S  —  P  .-.8  ^  P 

tubpra turn  pra  prat turn  tub  ttib turn  prce  tub. 

This  last  line  is  a  useful  mnemonic,  without  any 
other  meaning. 

The  first  figure  serves  especially  to  establish 
general  propositions.  The  universal  aflB.rmative  A 
can  be  proved  only  in  this  figure.  It  has  been 
sufficiently  illustrated  in  foregoing  examples. 

The  second  figure,  whose  conclusion  is  always 
negative,  is  especially  adapted  to  proving  differ- 
ences, and  so  clearing  obscure  thought  (§  21).  For 
example : 

The  true  apostles  were  not  thieves; ana 

Judas  was  a  thief; afi 

.'.  Judas  was  Dot  a  true  apostle ana 


FIGURE    AND    MOOD  121 

The  third  figure,  whose  conclusion  is  always  par- 
ticular, is  especially  adapted  to  bringing  in  exam- 
ples, and  thus  proving  an  exception  to  some  uni- 
versal statement.     For  example : 

The  apostles  sought  no  temporal  reward  ; ana 

The  apostles  were  zealous  in  their  work  ; af  i 

/.Some  zealous  persons  did  not  seek  temporal  reward ina 

This  contradicts,  and  so  disproves,  All  zealous  per- 
sons seek  temporal  reward.  Only  in  the  third  fig- 
ure can  the  middle  term  be  individual ;  for  in  each 
of  the  others  the  middle  term  is  once  at  least  a 
predicate,  and  an  individual  cannot  be  predicated 
(§  54).     For  example : 

Peter  was  an  inspired  man  ; af  1 

Peter  was  unlearned ; afi 

/.  Some  one  unlearned  was  inspired ifl 

The  fourth  figure  is  reserved  for  subsequent  and 
special  examination  (§  102). 

§  97.  By  deduction  from  the  General  Rules  of  the 
syllogism  (§  94)  we  obtain,  relative  to  the  several 
figures,  certain  Special  Rules,  as  follows : 

Example.  Special  Rula. 

Fig.  1  {sub  pra). 

No  man  is  perfect Major  premise  must  be  universal. 

(Else  undistributed  middle. ) 
Some  saints  are  men Minor  premise  must  be  affirma- 
tive.    (Else  illicit  major.) 
.'.  Some  saints  are  not  perfect . 

Fig.  2  iprmprcB). 

No  perfect-one  is  a  man Major  premise  must  be  universal. 

(Else  illicit  major.) 

Some  saints  are  men One  premise  must  be  negative. 

(Else  undistributed  middle.) 
.'.  Some  saints  are  not  perfect .  (Hence  the  conclusion  is  always 

negative,  Rule  4.) 


122  DEDUCTION 

Example.  SpecieU  Rula. 

Fig.  8  (sub  sub). 
No  man  is  perfect. 

Some  men  are  saints Minor  premise  must  be  aflSrma- 

tive.     (Else  illicit  major.) 
.'.Some  saints  are  not  perfect. Conclusion   must  be  particular. 

(Else  illicit  minor.) 
Fig.  4  (prce  sub). 

No  perfect-one  is  a  man If  either   premise   be    negative, 

major     must     be     universal 
(Else    illicit    major.) 

Some  men  are  saints If  major  premise  be  affirmative, 

minor      must     be     universal. 
(Else   undistributed   middle.) 
.'.Some  saints  are  not  perfect. If  minor  premise  be  affirmative, 

conclusion  must  be  particular. 
(Else  illicit  minor.) 

These  rules,  and  their  proof,  should  be  thoroughly 
examined ;  but  only  those  of  the  first  figure  need 
be  retained  in  memory.  All  have  reference  to  ex- 
tension. To  adapt  them  to  the  intensive  syllogism, 
it  is  needful  only  to  change  the  word  ma^or  to 
minor.,  and  vice  versa,  wherever  they  occur.  The 
symbolic  notation  of  the  example  above  is  the 
same  for  each  of  the  four  figures;  the  graphic 
notation  is  different  for  each  of  the  figures ;  thus — 

M 


Saints 


M  —  ,  S    (Fig.  1.) 

I       ■ 


§  98.  The  four  figures  of  the  syllogism  are  sub- 
divided into  moods,  upon  the  ground  of  the  quan- 
tity and  quality  of  the  premises.  The  conclusion 
need  not  be  taken  into  account,  since  it  is  deter- 
mined by  the  premises.  A  method  of  ascertaining 
the  moods  is  as  foUows : 


FIGURE   AND   MOOD  123 

Kelative  to  quantity  and  quality,  we  recognize 
four  propositions,  A,  E,  I,  O.  These,  as  premises, 
taken  two  at  a  time,  yield  sixteen  possible  combi- 
nations, exhibited  in  the  following  scheme : 

AA  Figs.  1,  3,  4.  EA  Figs.  1,  2,  3,  4. 

AE      "     2,  4.  [EE]  Sd  Gen.  Rule. 

AI        "     1,  3.  EI  Figs.  1,  2,  3,  4. 

AO  Fig.  2.  [EO]  3d  Gen.  Rule. 

lA    Figs.  3,  4.  OA  Fig.  3. 

[IE]  6th  Gen.  Rule.  [OE]  3d  Gen.  Rule. 

[II]   7th   "        "  [01]  7th  "        '• 

[10]  7th    "        "  [00]  3d    "        " 

But  not  all  these  combinations  will  yield  con- 
clusions, for  they  do  not  all  represent  the  premises 
of  valid  syllogisms.  Those  bracketed  are  to  be 
eliminated  as  violative  of  the  General  Rules.  Eight 
(one  half)  remain  as  valid,  since  they  accord  with 
the  General  Rules. 

Let  us  now  inquire  in  which  of  the  four  figures 
each  of  these  eight  valid  combinations  may  occur. 
We  apply  the  Special  Rules,  and  find  that  EA  and 
EI  accord  with  all  these  rules,  and  therefore  can 
appear  in  each  of  the  four  figures,  as  indicated  in 
the  scheme.  The  figures  in  which  the  others  can 
appear  are  similarly  ascertained  and  indicated. 
Upon  counting,  we  find  there  are  nineteen  valid 
moods  of  the  syllogism. 

§  99.  The  first  figure  has  the  mood  A  A.  Kow 
annex  the  symbol  of  the  conclusion,  and  coin  a 
word  containing  the  three  vowels  consecutively  as 
the  name  of  the  mood,  thus :  Barbara.   The  several 


124  DEDUCTION 

moods  are  treated  in  this  manner,  and  the  names 
of  the  nineteen  moods  thus  coined  are  arranged  in 
the  following  mnemonic  hexameters : 

Barbara,  Celarent,  Darii,  Ferio  que  prions; 
Cesare,  Camestres,  Festino,  Baroco'  secuncUe; 
Tertia  Darapti,  Disamis,  Datiai,  Felapton, 
Bocardo,-  Ferison  hahet.     Quarta  insuper  addit 
Bramantip,  Cameues,  Dimaris,  Fesapo,  Fresison. 

* — or  Dokamok,  '— orFakofo. 

or  Fokmafokf. 

These  names  of  the  moods  are  very  convenient. 
By  applying  its  name  to  any  reasoning,  we  at  once 
indicate  its  figure,  and  the  quantity  and  quality  of 
each  proposition,  and  also,  as  will  be  seen,  its  rela- 
tion to  other  moods  to  which  it  may  be  reduced, 
and  the  method  of  reduction.  Moreover,  they 
serve  as  a  test ;  for,  since  these  are  all  the  valid 
moods,  when  we  have  a  simple  syllogistic  form  to 
which  none  of  the  names  is  applicable,  we  know 
at  once  that  the  reasoning  is  false. 

From  the  conclusions  it  appears  that  each  of  the 
four  judgments  is  proved  in  Fig.  1.  Its  four  moods 
are  reducible  to  two,  the  third  and  fourth  being 
varieties  of  the  first  and  second.     Thus : 

Barbara  or  Darii.  Cdarent  or  Ferio. 

All  M  is  P  ;  No  M  is  P  ; 

All  or  some  S  is  M ;  All  or  some  S  is  M ; 

.*.  All  or  some  S  is  P.  .*.  No  S  is  P, 

or  Some  S  is  not  P. 

Here  is  one  positive  and  one  negative  form.  Since 
all  the  other  moods  may,  as  we  shall  find,  be  re- 
duced to  one  or  the  other  of  these,  they  are  the 
two  fundamental  forms  of  all  reasoning.     The  evi- 


FIGURE   AND    MOOD  125 

dence  of  this,  furnished  by  reduction,  is  perhaps 
the  chief  merit  of  the  system. 

Again,  on  noting  the  conclusions  throughout,  it 
appears  that — 

A  is  proved  in  1  figure  and  in  1  mood  whose  initial  letter  is  B. 
E  "  3  figures      "      4  moods     "         «  "  C. 

I  "  3  figures      "      6  moods     "         «  «  D.« 

O  "  4  figures      "      8  moods     "         "  "  F.* 

'  Except  Bramantip.  '  Except  Baroco  and  Bocardo. 

Hence  the  proposition  A  is  the  hardest  to  estab- 
hsh,  and  the  easiest  to  overthrow ;  and  O  is  the 
easiest  to  establish,  and  the  hardest  to  overthrow. 

§  100.  Reduction  is  of  two  kinds.     First,  Osten-  £. 
sive  Reduction.     A  syllogism  in  any  other  mood 
may  be  ostensively  reduced  to  one  or  another  of 
the  first  four,  and  thus  brought  under  the  syllogis- 
tic canon  (§  93).     The  initial  consonant  of  each 
name  is  that  of  the  mood  in  Fig.  1,  to  which  it 
reduces.     Baroco  and  Bocardo  are  exceptions,  but 
may  be  replaced  by  their  alternates.   The  reduction 
is  accomplished  by  substituting  for  one  or  more  of 
the  propositions  an  immediate  inference  from  it. 
Other  consonants  in  the  name  direct  us  in  doing  this. 
s  indicates  that  the  proposition  symbolized  by 
the  vowel  that  precedes  it  is  to  be  converted 
simply. 
p  indicates  that  the  preceding  proposition  is  to 
be  converted  per  accidens.     (Except  in  Bra- 
mantip, where  it  shows  that,  after  converting 
simply,  a  universal  is  warranted  by  the  prem- 
ises.    This  is  the  reverse  of  per  accidens.) 


126  DEDUCTION 

k  indicates  conversion  by  contraposition^ 

t  indicates  infinitation. 

m  indicates  that  the  premises  are  to  be  trans- 
posed {mutari). 

The  consonants  b,  d,  1,  n,  r,  t,  are  not  significant, 
but  are  inserted  merely  for  the  sake  of  euphony, 
or  for  metrical  quantity. 

The  following  examples  will  sufficiently  illus- 
trate the  process : 

Fig.  2,  Camestres,  reduces  to  Fig.  1,  Celareni. 

AllPisM;  No  Mis  S; 

NoSisM;  All  P  is  M; 

.-.No  S  is  P.  .-.No  P  is  S. 


C»m-  Every  wicked  man  is  discont'd ;  J  |  Ce-  No  discontented  man  is  happy; 
es-  No  happy  man  is  discontented;  f  =  ^  •»-  Every  wicked  man  is  discont'd; 
tres.    .•.  No  happy  man  is  wicked.  )       '  rent.  /.  No  wicked  man  is  happy. 

Fig.  3,  Darapli,  reduces  to  Fig.  1,  Darii. 

Da-    All  wits  are  dreaded ;  \        |  Da-     All  wits  are  dreaded; 

rap-    All  wits  are  admired;  f  ~  )   ""*"      Some  who  are  admired  are  wits; 

tl.  .-.Some  who  are  adm'd  are  dreaded.  )        (    I.  .-.  Some  who  are  adm'd  are  dreaded. 

Fig.  2,  Fakofo,  redaces  to  Fig.  1,  Ferto. 

Fak-  All  murders  are  intentional;  \        i    Fe-    No  unintent'l  things  are  murders; 

of-     Some  homicides  are  not  intent'l;    >■  = -<    ri-     Some  homicides  are  unintent'l; 
O.    .'.Some  homicides  are  not  murders.  )        (    o-  .'.  Some  homicides  are  not  murders. 


If  in  a  given  syllogism  a  proposition  requiring 
conversion  in  order  to  reduction  be  an  individual 
proposition,  then  the  reduction  is  not  practicable, 
for  an  individual  proposition  cannot  be  convert- 
ed (§  82). 

Moods  having  the  same  initial  letter  conclude 
the  same  formal  judgment.  The  only  exception  is 
Bramantip,  for  Baroco  and  Bocardo  have  alternates 
InF. 

Moods  having  the  same  initial  are  equivalent 
moods,    being    generally    reducible    to    each    other 


FIGUKE   AND    MOOD  127 

by  the  following  General  Rule  for  Reduction. 
Cause  the  propositions  to  appear  as  required 
by  any  legitimate  inference  from  them,  trans- 
posing, if  need  be,  the  premises. 

§  101.  The  ostensive  reduction  just  explained 
could  not,  it  was  believed,  be  applied  to  the  two 
moods  Baroco  and  Bocardo,  having  a  premise  in 
O.  Hence  the  early  logicians  devised  the  Reductio 
ad  impossihile.  It  is  a  test  of  the  validity  of  rea- 
soning from  granted  premises  in  those  two  moods. 

B,  the  initial  letter,  shows,  not  that  the  syllogism 
is  reduced  to  Barbara,  but  that  Barbara  is 
used  in  making  the  test. 

c  indicates  that  the  proposition  preceding  it  is 
to  be  omitted,  and  the  contradictory  of  the 
conclusion  substituted.  This  gives  premises 
in  Barbara,  from  which  a  new  conclusion  is 
drawn.     E.  g. : 

Baroco,  tested  by  Barbara. 

Ba-     All  murders  are  intentional;  (1)  Bar-    All  murders  are  intentioDal;  (4, 

roc-    Some  homicides  are  not  inteul'l;   (2)^s^^^  l)a-      AH  homicides  are  mfrders;  (5; 

(l   .'.Some  homicides  are  not  murders.  (3)  y«^^^  ra.    /.All  homicides  are  intent'l  (O; 

Here  the  conclusion  dra^vn  in  Barbara  (6)  is  false, 
because  it  contradicts  a  granted  premise  (2).  Hence 
a  premise  in  Barbara  is  false  (§  91).  But  one  of 
these  (4)  having  been  granted  (1),  the  false  one 
must  be  the  one  substituted  (5).  Now,  this  false 
proposition  being  the  contradictory  of  the  origi- 
nal conclusion  (3),  that  conclusion  must  be  true, 
and  this  reasoning  in  Baroco  valid.     So  also : 


128  DEDUCTION 

Bocardo,  tested  by  Barbara. 

Boc-       Most  men  do  not  weep;  (2)  K    ^  Bar-      All  who  feel  weep;  (6) 

ar-        All  men  feel;  (1)     V     ba-        All  men  feel;  (4) 

do.    /.  Many  who  feel  do  not  weep.  (3)  /\    ra.     .•.  All  men  weep.  (6) 

It  is  sufficient  to  say  :  If  we  contradict  the  con 
eluding  O,  then  by  plain  proof  (Barbara)  we  con- 
tradict the  premised  O,  which  is  absurd,  being  a 
self-contradiction. 

All  the  other  moods  may  be  tested  by  the  same 
process.  But  even  in  the  case  of  Baroco  and  Bocar- 
do it  is  superfluous.  The  former  can  be  reducea 
to  Fig.  1  by  using  its  alternate  Fakof o ;  the  latter 
by  Dokamok  (§  82).  But  since  Bocardo  concludes 
O,  it  should  reduce,  not  to  Darii,  but  to  Ferio. 
Therefore  we  propose  Fokmafokf  as  a  preferable 
alternate. 

Viewing  reduction  as  a  means  of  testing  the 
validity  of  syllogisms,  then  : 

Ostensive  reduction  is  direct  reduction,  and  indirect  test; 
Reduction  ad  impossibile  is  direct  test,  and  indirect  reduction. 

§  102.  The  fourth  figure  is  open  to  just  and  fatal 
criticism.     The  general  form  (§  96)  is : 

M^  S 
.-.  S  ^P 

But  observe  that,  in  the  affirmative  form,  P  being 
the  major  term,  the  premises  are  impossible.  The 
greater  cannot  be  contained  under  the  less.  But 
if  S  be  the  major  term,  we  directly  conclude  P  -^  S. 
This  is  Fig.  1,  t.  p.  Then  we  may  convert  the  con- 
clusion per  accidens,  or  else  simply,  and  get  Some 


FIGURE   AND   MOOD  129 

S  —  P.  The  procedure  is  evidently  compound, 
which  forbids  Bramantip  and  Dimaris  taking  rank 
with  the  simple  moods.  In  thought  they  are  Bar- 
bara and  Darii,  with  transposed  premises,  which 
is  arbitrary  (§  86),  and  a  subsequently  converted 
conclusion.  For  similar  reasons,  Camenes  is  Ce- 
larent. 

Fesapo  and  Fresison  are  even  more  faulty.  The 
direct  conclusion  is  illicit  major,  which  is  corrected 
by  a  conversion  jper  accidens.  Th  is  passage,  through 
a  fallacy,  is  of  course  inadmissible. 

Therefore,  the  moods  of  the  fourth  figure  should 
be  rejected  as  not  co-ordinate  with  the  others,  as 
superfluous,  and  in  two  cases  erroneous. 

§  103.  Praxis.  Write  a  detailed  proof,  based  on 
the  General  Rules,  of  the  three  following  points : 

1.  Prove  that  the  conclusion  in  Fig.  3  must  be  particular. 

2.  Prove  that  the  major  premise  in  Fig.  1  must  be  uni- 

versal. 

3.  Prove  that  from  IE  no  conclusion  is  valid. 

Name  the  moods  expressed  by  these  notations : 

4.  P  ^  :  M  ^ ,  S       6.  P  -H ,  M  :  ^  S       8.  P  -H:M,^  S 

5.  P  :^M^:  S       7.  P,  ^  M  :  ^'  8       9.  P  :^Mh«!  S 

In  the  following  examples  the  agreed  order  of 
the  propositions  is  preserved.  Redress  each  in 
strict  syllogistic  form,  supplying  any  lacking  prop- 
osition, and  name  its  mood.  Then  write  its  graphic 
notation.  Then,  if  it  be  not  in  Fig.  1,  reduce  it 
9 


130  DEDUCTION 

thereto.     To  Baroco  and  Bocardo  apply  the  test 
per  impossihile. 

10.  Whoever  possesses  prudence  possesses  all  virtue  ; 
Whoever  possesses  one  virtue  must  possess  pru 

dence. 

11.  Prudence  has  for  its  object  the  benefit  of  indi- 

viduals ; 
But  prudence  is  a  virtue. 

12.  No  good  action  results  in  evil ; 
Some  alms-giving  results  in  evil. 

13.  All  abstract  studies  strengthen  the  intellect; 
Exercises  that  strengthen  the  intellect  are  profitable. 

14.  No  science  is  capable  of  perfection ; 
All  science  is  worthy  of  culture. 

15.  No  vicious  conduct  is  praiseworthy  ; 
All  heroic  conduct  is  praiseworthy. 

16.  All  pride  is  inconsistent  with  religion; 
Some  pride  is  commended  by  the  world. 

17.  All  true  philosophers  account  virtue  a  good  in  itself ; 
The  Epicureans  do  not  account  virtue  a  good  in 

itself. 

18.  A  fallacious  argument  is  not  a  legitimate  mode  of 

pea"suasion ; 
A  legitimate  mode  of  persuasion  sometimes  fails  to 
convince ; 
.".  Not  all  those  arguments  are  fallacious  that  fail. 

19.  Every  candid  man  acknowledges  merit  in  a  rival; 
Every  learned  man  does  not  do  s* ; 

.'.  Every  learned  man  is  not  candid. 


FIGURE   AND   MOOD  131 

20.  A  few  men  at  least  are  truly  honorable,  yet  all  have 

imperfections ;  hence  some  are  so  who  have  im- 
perfections. 

21.  All  expedient  acts  are  conformable  to  nature ; 
Nothing  conformable  to  nature  is  hurtful  to  society. 

22.  Nothing  that  must  be  repented  of  is  desirable.    Now 

many  of  our  most  intense  enjoyments  constrain 
repentance.  Few  of  these,  then,  are  truly  de- 
sirable. 

23.  There  is  no  growth  without  sunshine,  and  these 

flowers,  being  deprived  of  it,  will  not  grow. 

24.  What  is  not  in  Scripture  is  not  binding  on  con- 

science ; 
Since  many  ecclesiastical  canons  are  not  found  there- 
in, they  may  be  disregarded. 

25.  No  virtue  is  a  natural  quality ; 

Every  natural  quality  has  God  for  its  author. 

.  26.  Some  kinds  of  anger  are  not  unrighteous ; 
Every  kind  of  anger  is  a  passion. 

27.  Some  of  our  tax-laws  are  oppressive  measures; 
All  oppressive  measures  should  be  repealed. 

28.  Prejudices  are  in  no  case  compatible  with  perfection  j 
Yet  some  are  quite  innocent. 

29.  All  wicked  men  are  discontented; 
Socrates  is  not  discontented. 


v.— MODIFIED    FORMS 

§  104.  The  various  modes  in  which  reasonings 
may  be  expressed  are  endless.  Except  in  treatises 
on  logic,  it  is  rare  that  a  formal  syllogism  occurs. 
In  conversation,  or  even  in  argumentation,  its  pres- 
ence is  offensive,  for  an  intelligent  hearer  does  not 
need  complete  statement,  a  hint  being  often  suffi- 
cient. Unnecessary  words  do  not  elucidate,  but 
obscure,  thought.  It  is  usual,  then,  to  abbreviate 
expression.  Even  essential  propositions,  if  they 
be  obvious,  are  elided ;  often  they  are  compounded 
or  condensed,  so  that  the  thought  is  rarely  stated 
entire,  or  in  strictly  logical  order.  We  propose 
now  to  illustrate  some  of  these  modified  forms. 

An  Enthymeme  is  an  incomplete  syllogism, 
one  or  two  judgments  being  unexpressed.  There 
are  four  orders  : 

1st.  The  major  premise  unexpressed.  This  oc- 
curs most  frequently  because  the  sumption  is  very 
often  a  general  rule  understood  and  admitted, 
whereas  the  subsumption  is  often  a  question  of 
fact  which  needs  to  be  stated  and  established,  in 
order  to  be  subsumed.  E.  g.,  Yonder  celestial  body 
has  a  proper  motion  among  the  fixed  sta/rs'j  there' 
fore  it  is  a  memher  of  the  solar  system. 


MODIFIED   F0BM8  133 

2d.  The  minor  premise  unexpressed.  This  gives 
emphasis  to  the  conclusion.  E.  g.,  Pra/yers  are  often 
sinful;  for  whatsoever  is  not  of  faith  is  sin. 

3d.  The  conclusion  unexpressed.  Sometimes  this 
is  high  art.  The  speaker  does  not  formally  com- 
mit himself,  the  hearer  draws  the  conclusion,  as  in 
the  famous  speech  of  Antony  over  the  body  of 
Caesar.  E.  g.,  Virtue  is  alwoAjs  discreet;  hut  there  is 
a  zeal  without  discretion. 

4th.  Only  one  judgment  expressed.  When  we 
see  on  a  tombstone  The  memory  of  the  just  is 
hlessed,  the  implied  syllogism  is  manifest.  This 
form  often  occurs  in  texts,  proverbs,  pithy  sayings, 
and  in  witticisms.  If  some  one,  seeing  me  vexed, 
should  say.  The  way  of  the  tra/nsgressor  is  hard, 
I  am  indignant,  for  the  implied  syllogism  concludes 
me  a  transgressor,  and  that  through  an  undistrib- 
uted middle.  This  was  precisely  the  argument  of 
Job's  comforters.  Sometimes  this  form  is  an  in- 
sinuation, as  when  Falstaff  replies  to  Prince  Hal, 
Lord^  Lord,  how  this  world  is  gi/ven  to  lying  /  The 
answer  to  a  question  is  often  indirect,  merely  giv- 
ing a  premise  which  authorizes  the  doubtful  prop- 
osition. E.  g..  Is  smuggling  a  crime  f  Ans.,  What- 
ever violates  the  rights  of  society  is  a  crime.  The 
message  to  Pilate  from  his  wife  may  be  taken  as 
an  instance  of  a  single  word  hinting  premises  sup- 
porting the  hortatory  conclusion :  HoA^e  thou  noth- 
ing to  do  with  that  just  mom.  Finally,  when  the 
disciples  of  John  asked  our  Lord,  Art  thou  he  that 
should  come  ?  he  replied  indirectly,  giving  them  a 


134  DEDUCTION 

minor  premise,  not  in  words,  but  in  deeds.  In  that 
same  hour  he  did  many  miracles,  and  bade  the  dis- 
ciples tell  John  what  they  had  seen. 

§  105.  An  Epichirema,  or  reason-rendering  syl 
logism,  is  one  that  has  attached  to  either  premise, 
or  to  both,  a  supporting  reason.  That  is  to  say,  it 
is  a  syllogism  having  for  a  premise  the  conclusion 
of  an  enthymeme.  This  enthyraeme  may,  of  course, 
be  expanded  into  a  syllogism.  A  syllogism  whose 
premise  is  the  conclusion  of  another  is  called  an 
Episyllogisra,  One  whose  conclusion  is  the  premise 
of  another  is  called  a  Prosy Uogism.    For  example : 


Episyllogism.  Prosyllogism. 

Vice  is  odious ;  (       Whatever  enslaves  is  a  vice ; 

Avarice  is  a  vice ;  for  it  enslaves ;  =  <       Avarice  enslaves ; 
.  Avarice  is  odious.  f  .'.  Avarice  is  a  vice. 


The  propriety  of  thus,  in  the  progress  of  an  argu- 
ment, offering  some  reason  or  reasons  in  support 
of  its  doubtful  propositions  is  apparent.  By  so 
doing  we  avoid  the  necessity  of  returning  over  the 
game  ground ;  and  by  clearing  doubts  as  we  go 
along,  we  are  not  so  likely  to  excite  in  the  hearer 
the  disgust  that  comes  of  suspense. 

§  106.  A  Sorites  is  a  chain  of  enthymemes, 
holding  throughout  the  relation  of  prosyllogism  to 
episyllogism.  It  is  expressed  either  intensively  or 
extensively.  The  difference  between  the  two  forms 
as  to  the  order  of  premises  is  merely  conventional, 
not  essential  (§  86). 


MODIFIED   FORMS 


135 


Scheme  of  Sorites. 


Progressive  form, 
in  intension. 


A^  B 
B  ^  C 
C  — D 

I     i>  ^  i<: 

I  .-.A -HE 


Regressive   form, 
in  extension. 


dh-e 

C^  D 
B^  C 
A^  B 

.ah-e 


Resolution  of  the  progressive  form. 

a  is  c; 

Cis  D; 

.'.  a  is  d. 

Resolution  of  the  regressive  form. 

D  is  not  E ;  c  is  not  e ; 


Ais  B; 
Bis  C; 
.  a  is  c. 


CisD; 
.c  is  not  e. 


BisC; 
.'.  b  is  not  e. 


a  is  d; 
D  is  not  E ; 
'.A  is  not  E. 

b  is  not  e ; 
A  is  B; 
;.  A  is  not  E. 


Example. 
Some  who  are  prosperous  are  avaricious; 
The  avaricious  are  intent  on  gain; 
The  intent  on  gain  are  discontented; 
f  he  discontented  are  not  happy ; 
^ome  who  are  prosperous  are  not  happy. 

Notation  in  depth. 


Example. 
No  discontented  men  are  hnppy  men; 
All  men  intent  on  guiu  are  discont'd  men; 
All  avaricious  men  are  men  intent  on  gain 
Some  prosperous  men  are  avaricious  men; 
.-.Some  prosperous  men  are  not  happy  men 

Notation  in  breadth. 


Other  notations  in  hreadth. 
happy  men 


discontented  men 
men  intent  on  gain 


pros 


avaricious  men 


perous  men 


The  following  points  should  be  carefully  noted 
and  analyzed : 

1st.  The  regular  Sorites  has  as  many  middle 
terms,  and  hence  resolves  into  as  many  syllogisms, 
as  it  has  premises,  less  one. 

2d.  The  first  proposition  is  the  only  major  prem- 
ise expressed ;  the  other  premises  are  minors. 


136  DEDUCTION 

.  3d,  Each  unexpressed  major  premise  is  the  con- 
clusion of  the  preceding  syllogism. 

4th.  Only  one  premise  may  be  negative,  and 
this  must  come  last  in  intension,  and  first  in  ex- 
tension ;  else  illicit  process. 

5th.  Only  one  premise  may  be  particular,  and 
this  must  come  first  in  intension,  and  last  in  exten- 
sion ;  else  undistributed  middle. 

We  also  remark  that  in  the  scheme  all  the  syllo- 
gisms are  in  Fig.  1.  A  sorites  cannot  occur  in  the 
other  figures  throughout.  One  step,  however,  may 
be  in  Fig.  2  or  Fig.  3,  but  only  one,  and  it  must  be 
either  the  first  or  the  last. 

§  107.  Arguments  are  frequently  stated  in  what 
at  first  glance  appears  to  be  a  single  simple  syllo- 
gism, but  which  a  slight  inspection  discovers  to  be 
compound,  or  to  involve  some  deviation  from  rule. 

When  a  conclusion  is  a  compound  proposition, 
it  is  evident  that  there  must  be  at  least  one  com- 
pound premise,  and  that  the  statement  involves 
two  or  more  syllogisms.     For  example : 

The  triumvirs  were  ambitious; 
Caesar,  Pompey,  and  Crassus  were  triumvirs; 
.•.Caesar,  Pompey,  and  Crassus  were  ambitious. 

Here  are  obviously  three  syllogisms  involved  in 
one  statement.  If  we  substitute  for  the  major 
term  founded  the  empire^  then  there  is  but  one, 
since  the  change  makes  all  the  propositions  simple. 
When  the  conclusion  is  simple,  a  compound  prem- 
ise involves  a  surplus  of  matter.     For  example : 


MODIFIED    FORMS  137 

Whatever  revolves  about  the  earth  must  present  phases  i. 
The  moon  alone  revolves  about  the  earth; 
/.The  moon  makes  phases. 

This  coTnpound  minor  premise  resolves  into  The 
moon  revolves  ahout  the  earth,  from  which  tlie  con- 
clusion follows,  and  What  is  not  the  moon  does  not 
revolve  ahout  the  earth,  from  which  no  conclusion  is 
competent,  since  it  would  give  illicit  major.  Hence 
more  is  contained  in  the  premises  than  can  be  col- 
lected in  the  conclusion. 

But  a  compound  exponible  premise  in  other  cases 
may  yield  a  compound  conclusion  collecting  all 
that  is  given.     For  example  : 

Justification  comes  by  faith  alone; 
Our  highest  hope  is  justification; 
.'.Our  highest  hope  comes  by  faith  alone. 

This  may  be  resolved  into  two  simple  syllogisms, 
Barbara  and  Celarent.  But  it  is  not  requisite,  for 
we  may  view  comes  hy  faith  alone  as  simply  the 
major  term,  and  the  whole  as  Barbara. 

There  is  a  class  of  disguised  syllogisms  in  which 
the  premises  are  irregularly  stated.  They  consist 
of  simple  propositions  indeed,  but  require,  in  order 
to  bring  them  under  logical  rule,  the  substitution 
of  equipollent  propositions,  or  else  of  one  or  more 
subsidiary  inferences.  In  some  cases  the  resolution 
is  obvious.    For  example : 

The  sun  is  a  thing  insensible; 
The  Persians  worship  the  sun; 
.'.The  Persians  worship  a  thing  insensible. 

Here  are  five  terms;  yet  the  reasoning  is  evicient- 


138  DEDUCTION 

\y  very  good.  The  canon  of  replacement  is  di- 
rectly applicable,  the  conclusion  being  obtained  by 
replacing,  in  the  minor  premise,  the  sun  by  its  un- 
distributed genus,  a  thing  insensible,  as  declared  in 
the  major  premise.  But  even  under  the  common 
logical  rules  the  resolution  is  very  simple.  From 
the  major  premise  we  may  immediately  infer,  by 
determination  (§  80),  They  loho  worship)  the  sun 
worship  a  thing  insensible,  and  we  then  have  a  per- 
fectly regular  Barbara. 

The  following  would  hardly  puzzle  a  tyro : 

Whoever  probes  a  wound  is  on  the  verge  of  crime ; 
A  wound  is  probed  by  the  healer ; 
.'.The  healer  is  on  the  verge  of  crime. 

For  the  passive  minor,  substitute  the  equipollent 
active  form  (§  78),  The  healer  probes  a  wound,  and 
we  have  again  Barbara. 

An  example  involving  an  immediate  inference  in 
opposition  is  as  follows  : 

That  riches  are  often  a  bitter  curse  is  true ; 
And  yet  it  is  also  true  that  most  men  desire  riches ; 
.'.It  is  false  to  say  that  no  men  desire  what  is  often  a  bit- 
ter curse. 

The  syllogism  which  is  here  slightly  disguised  is  the 
following  Darii : 

They  who  desire  riches  desire  what  is  often  a  bitter  curse ; 

Most  men  desire  riches  ; 
.'.Most  men  desire  what  is  often  a  bitter  curse. 

This  major  premise  is  immediately  inferred  by  de- 
termination ;  the  conclusion,  by  opposition ;  for  if 
E  be  false,  then  I  is  true. 


MODIFIED   FORMS  139 

§  108.  There  are  certain  modes  of  procedure  in 
argument  which,  though  strictly  belonging  under  a 
doctrine  of  method,  may  fairly  be  mentioned  here. 

The  argumentum  ad  rem  is  the  direct  or  osten- 
sive  proof  of  the  thesis,  or  problem,  or  main  point 
in  question,  the  qucesitum. 

In  order  to  such  procedure,  premises  must  be 
had.  To  assume  them  without  proof  is  to  beg  the 
question  or  principle,  petitio  prindpii  (§  146).  If 
they  be  granted  argumenti  gratia^  or  allowed  as 
unquestionable,  the  procedure  is  legitimate.  But 
whence  come  unquestionable  premises?  To  say 
they  are  conclusions  of  precedent  inferences  is  in- 
sufficient, for  the  question  recurs  as  to  these.  The 
answer  is  that  ultimately  they  are  derived  from 
pure  intuition  or  from  experience,  the  two  original 
sources  of  all  knowledge. 

When  the  ultimate  premises  are  intuitive  princi- 
ples, self-evident  truths,  axioms,  the  procedure  is 
a  priori.  So  from  the  axiom,  Two  straight  lines 
cannot  enolose  an  area,  geometry  is  evolved ;  from 
the  primary  laws  of  thought,  logic ;  from  the  mor- 
al law,  ethics.  The  syllogistic,  deductive  process 
a  priori  is  strictly  demonstrative,  apodeictic  (§  90). 
And  since  the  ultimate  premises  are  necessary 
truths,  the  conclusions  are  necessarily  true. 

"When  the  ultimate  premises  are  empirical,  or 
truths  of  experience,  they  have  been  obtained  a  pos- 
teriori. Thus  induction  infers  from  particular  facts 
of  experience  truths  of  empirical  universality,  and 
80  afifords  premises  for  subsequent  deduction  (§  77); 


140  DEDUCTION 

such  as  All  men  are  mortal,  and  The  volume  of  a 
gas  is  in  inverse  ratio  to  the  pressure.  Hence  arise 
the  inductive  sciences;  as  astronomy,  geology, 
physics.  Probable  or  moral  reasoning,  or  dialec- 
tics, always  involves  empirical  matter,  and  so  falls 
short  of  strict  demonstration. 

The  argumentum  a  fortiori,  which  may  be  taken 
as  one  variety  of  that  ad  rem,  and  understood  to 
mean/br  a  stronger  reason,  gathers  up  in  the  con- 
clusion an  additional  force  from  relations  in  the 
premises.  The  general  formula  is :  If  A  be  con- 
tained under  B,  and  B  under  C,  then  hy  so  much 
the  more  is  A  contained  under  C.  For  example : 
If  God  so  clothe  the  g7'ass  of  the  field,  shall  he  not 
much  more  clothe  you  f 

When  unquestionable  premises  as  a  basis  for 
direct  probation  are  not  available,  resort  is  often 
had  to  one  of  the  three  following  indirect  methods : 

The  argumentum  ad  verecundiaai^  is  an  appeal 
to  authority,  to  some  venerable  institution,  to  an- 
tiquity, etc.,  as  when  a  dictionary  is  allowed  to 
settle  the  disputed  meaning  of  a  word,  or  reference 
is  made  to  an  orthodox  creed. 

The  argumentum  ad  judicium  is  an  appeal  to  the 
judgment  or  common-sense  of  mankind.  We  hear 
it  often  in  conversation  in  the  phrases  Everyhody 
says,  and  No  one  thinks,  etc. 

The  argumentum  ad  populum  is  an  appeal  to 
principles  cherished  by  the  pubhc.  It  is  legiti- 
mate if  the  principles  be  sound.  But  an  appeal  to 
prejudice  or  passion  usually  betrays  weakness. 


MODIFIED    FORMS  141 

The  argumentum  ad  impossibile  or  reductio  ad 
ahsurdum  indirectly  proves  a  thesis  by  showing 
that  its  contradictory  is  absurd,  that  it  is  self-con- 
tradictory, or  contradictory  of  an  axiom  or  other 
admitted  principle,  as  in  §  101,  For  example,  In 
a  triangle  the  sides  opposite  two  equal  angles  are 
equal;  for  if  they  he  not  equal,  it  follows  that  a 
part  is  equal  to  the  whole,  which  is  absurd  (§  10), 
Likewise  it  is  used  in  disproof ;  as.  If  the  foot-tracks 
were  made  hy  the  prisoner,  he  was  wearing  shoes 
much  smaller  than  his  feet. 

The  argumentum  ad  hominem  is  arguing  from 
the  premises  of  an  opponent  merely  to  defeat  him. 
We  accept  his  principles  on  which  to  base  a  coun- 
ter-argument, even  if  believing  them  false,  our  ar- 
gument being  directed  against  him  personally,  ad 
hominem.  It  aims  to  convict  him  of  ignorance, 
bad-faith,  inconsistency,  or  illogical  reasoning,  and 
so  to  put  him  ex  curia.  Usually  it  attempts  no 
more.  Our  Lord  often  used  this  method  to  silence 
his  adversaries,  as  in  Matt.  xxii.  41-45.  Since  the 
argument  proceeds  ex  concesso,  it  is  formally  intro- 
duced by  a  concessive  proposition ;  as.  Though  one 
rose  from  the  dead  (Luke  xvii.  31) ;  and.  Though 
rich,  yet  not  therefore  happy,  for,  etc.  Criticism  is 
mostly  in  the  form  ad  hominem,  and  should  be  dis- 
tinguished from  proof  of  the  opposite  or  contro- 
versy. 

We  remarji,  finally  and  generally,  that  in  disproof 
the  attack  may  be  directly  on  the  thesis,  showing 


142  DEDUCTION 

it  to  be  false,  or  upon  the  argument,  showing  it  to 
be  from  a  false  premise,  or  else  illogical.  In  the 
two  latter  cases  the  result  is  merely  negative  (§  91), 
but  is  often  sufficient.  The  onus  probandi,  or  bur- 
den of  proof,  rests  ordinarily  upon  the  party  mak- 
ing  a  primary  assertion,  whether  positive  or  nega- 
tive. If,  however,  he  can  fairly  appeal  ad  verecim- 
diam  or  ad  judicium^  or  even  ad  jpopulum^  the 
logical  presumption  is  in  his  favor,  and  the  onus 
falls  on  the  disputant. 

§  109.  Praxis.  State  of  each  of  the  following 
examples  whether  it  is  a  simple  enthymeme,  or  an 
epichirema,  or  a  sorites.  Put  it  in  strict  logical 
form,  and  write  out  the  implied  syllogisms,  nttming 
the  mood.  In  case  of  an  epichirema,  distinguish 
the  pro-  and  epi-syUogism : 

1.  Blessed  are    the    merciful ;    for  they   shall   obtain 

mercy. 

2.  Cunning  cannot  be  a  virtue ;  for  no  virtue  degrades. 

3.  Every  man   should   be   moderate ;   for   excess  will 

cause  disease. 

4.  Kings,  having  no  equals,  have  no  friends. 

6.  Suppose  ye  that  these  Galileans  were  sinners  above 

all  the  Galileans,  because  they  suffered  such  things  ? 

I  tell  you  nay. 
6.  The  flesh  of  ruminants  is  good  for  food,  and  these 

animals,  since  they  have  horns  and  cloven  hoofs, 

belong  to  that  class. 
T.  What  if  a  rule  never  is,  and  a  principle  always  is,  a 

law  admitting  no  exception  ? 


//■ 


MODIFIED   FORMS  143 

.8.  Whatever  tends  to  withdraw  the  mind  from  pursuits 
of  a  low  nature  deserves  to  be  promoted.  This 
classical  learning  does,  since  it  cultivates  a  taste 
for  intellectual  enjoyments. 

9.  The  Scripture  narratives  are  trustworthy ;  because 
the  writers  had  the  means  of  knowing  the  facts; 
because  they  evidently  were  sincere  and  candid; 
and  because  the  narratives  are  consistent. 

10.  All   true   patriots   are   friends  to   religion,  religion 
being  the  basis  of  national  prosperity ;  but,  since 

their  lives  are  not  in  accordance  with  its  precepts, 
it  follows  that  some  great  statesmen  are  not  friends 
to  religion. 

11.  Lithium  is  an  element;  for  it  produces  an  alkali, 

therefore  is  a  metal,  and  hence  an  element. 

12.  I  will  not  do  this  act,  because  it  is  unjust ;  I  know 

tliat  it  is  unjust,  because  my  conscience  tells  me 
so ;  and  my  conscience  tells  me  so,  because  the  act 
is  wrong. 

Put  the  following  logical  climax  in  its  opposite 
form,  and  write  the  circular,  linear,  and  graphic 
notation : 

13.  The  prudent  are  temperate ; 

The  temperate  are  constant ; 
The  constant  are  unperturbed ; 

The  unperturbed  are  without  sorrow ; 
Those  without  sorrow  are  happy ; 
.'.  The  prudent  are  happy. 

— Seneca,  Epist.  85. 

Put  the  following  in  its  opposite  form,  and  write 
the  notation : 


144  DEDUCTION 

14.  Nothing  which  is  indissoluble  is  mortal ; 

What  has  no  composition  of  parts  is  indissoluble ; 
A  spirit  has  no  composition  of  parts ; 
A  thinking  substance  is  a  spirit ; 
The  mind  is  a  thinking  substance  ; 
.'.  The  mind  is  not  mortal. 

— Plato,  PhcBdo,  18. 

State  each  of  the  following  as  a  regular  sorites 
in  either  form  : 

1 6.  A  demagogue  must  hold  the  people  in  contempt ;  for, 
being  a  favorite,  he  must  know  how  to  manage 
them ;  therefore  he  understands  their  weaknesses, 
and  his  contempt  must  follow. 

16.  We  must  increase  the  income-tax ;  for  war  has  be- 

come a  necessity,  and  we  cannot  go  to  war  without 
money,  which  can  be  raised  only  by  taxation. 
But  the  only  tax  which  the  resources  of  the  coun- 
try can  bear  is  the  income-tax,  since  it  will  fall  on 
the  richer  part  of  the  population. 

Write  out  the  syllogisms  involved  in  the  follow- 
ing irregular  and  compound  forms,  supplying  any 
inference  that  may  be  lacking : 

17.  The  French  once  more  are  endeavoring  to  establish 

a  republic. 
A  republic  is  a  representative  government ; 
.'.  The  French  once  more  are  endeavoring  to  establish  a 
representative  government. 

18.  The  value  of  money  is  merely  a  purchasing  power; 
Interest  on  money  is  only  a  reward  of  abstinence ; 

.'.  Interest  on  money  is  not  the  value  of  money. 


MODIFIED    FORMS  145 

19.  Gladstone,  Argyll,  and  Disraeli  are  eminent  states- 

men; but  they  are  also  eminent  authors  ; 
.'.  In  some  cases   literary  success   is  not  inconsistent 
with  statesmanship. 

20.  They  are  out  of  the  reach  of  their  enemies  who  can- 

not be  robbed  of  what  they  love  ; 
He  cannot  be  robbed  of  what  he  loves  who  loves 
God  alone ; 
.*.  They  who  love  God  alone  are  out  of  the  reach  of 
their  enemies. 

21.  None  are  happy  but  the  virtuous; 

There  are  many  rich  men  who  are  not  virtuous ; 
.*,  There  are  rich  men  who  are  not  happy. 

22.  Every  one  desires  happiness ;  but  virtue  (alone)  is 

happiness ;  hence  every  one  desires  virtue. 

23.  The  true  philosopher  places  his  chief  happiness  in 

moral  and  intellectual  excellence. 
But  it  is  false  to  say  that   there  is   an   excellence 
without  activity ; 
.'.  His  chief  happiness  is  placed  by  the   philosopher 
in  moral  and  intellectual  activity. 

What  names  mark  the  following  reasonings : 

24.  If  any  objection  that  can  be  urged  would  justify  a 

change  in   the    established  laws,  no   laws   could 
reasonably  be  maintained. 

25.  That  used  in  Luke  v.  21 ;  and  its  answer. 

26.  That  used  in  Luke  xiii.  15-16  ;  and  in  John  x.  34-36. 

27.  Those  used  by  Demetrius  in  Acts  xix.  23-27  ;  and 

by  the  town-clerk  in  vers.  34-41. 

28.  Those  used  by  the  barbarians  in  Acts  xxviii.  3-6. 

29.  Those  used  by  Paul  in  Romans  v.  7-10. 

30.  That  used  by  Eliphaz  in  Job  iv.  17-19. 

10 


VI.— CONDITIONAL  PROPOSITIONS 

§  110.  The  word  condition  is  used  in  at  least 
three  several  and  important  senses,  as  follQ3a:sj 

1st.  A  real  condition  is  what  must  be,  that  some- 
thing else  may  be.  Here  must  indicates  conditio 
sine  qua  non,  or  necessitas  antecedentis.  E,  g.,  Jf 
space  is,  hody  may  he;  or,  more  fully.  Space  must 
he,  in  order  that  hody  rnay  he.  So  also.  Freedom 
must  he,  that  responsihility  may  he.  This  primary 
meaning  has  reference  to  reality  in  objects,  and 
therefore  is  metaphysical  rather  than  logical. 

2d.  A  causal  condition  is  what  determines  an 
event.  It  is  causa  essendi,  an  efficient  cause  of 
being — necessitas  consequentis.  E.  g..  If  force  is,  a 
change  is;  If  industry  is,  prosperity  is.  In  many 
specific  cases  the  condition,  because  of  an  apparent 
plurality  of  causes,  is  not  essential  or  sine  qua  non. 
Likewise  an  occasion  may  be  a  condition.  E.  g., 
If  repentance  is,  forgiveness  may  he;  If  peace  (a 
negative)  is,  prosperity  may  he.  Deductive  logic  is 
not  at  all  concerned  with  either  real  or  causal  con- 
ditionals. 

3d.  A  logical  condition  is  what  supports  a  cog- 
nition. It  is  causa  cognoscendi,  an  efficient  cause 
of    knowing,   a   reason  —  necessitas   consequentixB. 


CONDITIONAL    PROPOSITIONS  147 

Yery  often  a  real  or  a  causal  condition  or  an  oc- 
casion is  thought  merely  as  a  logical  condition. 
E.  g.,  If  space  is,  then  (I  know  that)  body  may  he  ; 
Jf  industry  is,  then  (I  know  \haX)  jprosperity  is;  If 
repentance  is,  (I  know  that)  forgiveness  may  he. 
The  inverted  real  and  the  inverted  causal  proposi- 
tions furnish  logical  conditions.  E.  g.,  If  hody  is, 
(I  know)  space  must  he ;  If  responsihility  is,  then 
freedom  must  he;  If  prosperity  is,  surely  there  is 
industry.  But  very  often  in  conditional  proposi- 
tions the  logical  relation  of  containing  and  con- 
tained, oi  a  reason  supporting  a  conclusion,  alone 
is  found.     E.  g.,  If  men  are,  rational  heings  are ; 

If  gold  is,  metal  is;  If he  a  man,  he  is  mortal. 

In  simple  forms  the  logical  condition  is  never  sine 
qua  non.    In  compound  forms  it  so  occurs. 

In  its  treatment  of  conditionals,  deductive  logic 
is  concerned  exclusively  with  the  logical  condition, 
with  propositions  expressing  the  relation  of  reason 
and  consequent. 

§  111.  The  distinction  between  categorical  and  "'' 
conditional  propositions  has  already  been  noted 
(§  58).     The  general  distribution  is  as  follows : 

(Categorical S  is  P,  and  S  is  not  P. 
r  Conjunctive;  If  A  be  B,  C  is  D. 
tkmal  J  Disjunctive;  C  is  either  D  or  non-D. 
(  Dilemmatic ;  If  A  be  B,  C  is  either  D  or  non-D. 

Hypothetical  is  synonymous  with  conditional,  and 
hypothesis  with  supposition.  The  dilemmatic  prop- 
osition, because  of  its  compound  character,  is  also 


1 48  DEDUCTION 

called  the  conjunctivo-disjunctive  proposition.  Con- 
ditional propositions  are  always  affirmative. 

t  §  112.  A  conjunctive  proposition  expresses  the 
relation  between  a  reason  and  its  consequent.  It 
has  two  clauses,  or  members.  The  subordinate 
clause  expresses  the  condition,  and  is  called  the 
hypothesis,  the  supposition,  the  protasis,  the  ante- 
cedent, or  the  reason.  The  principal  clause  ex- 
presses what  is  conditioned,  and  is  called  the  apod- 
osis,  or  the  consequent.  Usually  and  formally  the 
protasis  is  written  first,  but  inversions  often  occur. 
Existential  conjunctives  have  but  two  terms; 
formula,  If  A  is,  B  is ;  examples  in  §  110.  Another 
class  having  but  two  terms  will  be  noticed  pres- 
ently (§  116).  Conjunctives  involving  three  and 
four  terms  are  formulated  thus : 

1  (a)— If  A  be  B,  A  is  C ;  e.  g. ,  If  man  be  responsible,  he  is  free, 
(b) — If  Abe  B,  C  is  A;  e.  g.,  If  bliss  have  no  anxieties,  igno- 
rance is  not  bliss. 

(c)— If  A  be  B,  B  is  C ;  e.g.,  If  rubies  be  clay,  some  clay  is 

precious, 
(d) — If  A  be  B,  C  is  B ;  e.  g. ,  If   metals    be    fusible,   gold    is 

fusible. 

2  If  A  be  B,  C  is  D;  e.  g..  If  the  wise  be  virtuous,  Socrates 

was  innocent. 

In  each  of  the  first  forms  there  are  but  three  terms, 
one  being  common  to  both  members.  In  the  sec- 
ond there  are  four.  In  simple  sequence,  the  con- 
sequent only  or  both  clauses  may  be  negative  and 
may  be  particular ;  but  the  consequent  in  1  (b)  must 
be  negative,  and  in  1  (c)  must  be  particular. 


CONDITIONAL   PROPOSITIONS  149 

§  113.  A  disjunctive  proposition  expresses  the  i' 
relation  between  two  alternative  clauses  in  which 
one  must  be  true.  The  formula  is:  Either  C  is 
D,  or  C  is  non-D,  usually  abbreviated  as  in  §  111. 
One  clause  is  affirmed  on  condition  that  the  other 
be  denied.  In  general,  then,  the  condition  lies  in 
the  opposition  of  the  clauses.  The  opposed  clauses 
are  called  the  disjunct  members,  and  their  relation 
the  disjunction.  An  inverted  formula  is:  Either 
D  or  non-D  is  C. 

This  form  of  judgment  involves  the  principles, 
and  is  subject  to  the  laws  of  Division  (§  29  sq.)  and 
Opposition  (§  83).  It  implies  the  division  of  an 
unnamed  genus  into  co-ordinate  species,  and  affirms 
identity  between  an  object  or  a  class  of  the  genus 
and  one  or  the  other  of  the  species.  For  example : 
Carlo  is  either  a  dog  or  a  non-dog ;  or,  naming  the 
genus.  Carlo,  being  a  brute,  is  either  a  dog  or  a 
non-dog.  So  also.  Cares  are  either  distressing  or 
not,  all  under  the  genus  feelings ;  Every  action  is 
either  bond  (yr  free;  Either  now  or  later  will  suit 
me  very  well. 

Disjunctive  judgments,  to  be  strictly  logical, 
must  make  a  complete  disjunction;  that  is,  the 
disjunct  members  must  exhaust  the  divisum,  and 
be  exclusive  of  each  other.     For  example : 

Either  all  wars  are  evil,  or  some  wars  are  not  evil.       j ?££l^ff 

Either  the  prisoner  is  guilty,  or  he  is  not  guilty.  guilty    not  guilty 


The  members  are  contradictories  within  the  divided 
genus  or  logical  universe  (§  27).     The  law  of  con- 


150  DEDUCTION 

tradictory  opposites  is  that  one  must  be  true  and 
one  false ;  hence,  affirming  either  denies  the  other, 
and  denying  either  affirms  the  other. 

It  follows  that  a  disjunctive  resolves  into  four 
conjunctives,  thus : 

If  C  be  D,  it  is  not  non-D; 
If  C  be  non-D,  it  is  not  D; 
If  C  be  not  D,  it  is  non-D ; 
If  C  be  not  non-D,  it  is  D. 

Disjunctive  judgments  often  appear  in  the  form : 
Either  C  is  D,  or  M  is  N.  Here  the  matter  of  the 
opposed  clauses  is  entirely  distinct,  and  the  oppo- 
sition is  mediate,  evolved  thus : 

Either  Richard  III.  was  a  monster,  or  he  was  not  a 
monster; 
But  If  he  was  not  a  monster,  Shakespeare  was  wrong; 
Hence,  Either  Richard  III.  was  a  monster,  or  Shakespeare  was 
wrong. 

The  alternative  is  declared,  not  between  members 
directly  opposed,  but  between  one  of  these  and  a 
consequence  of  the  other. 

§  114.  "When  a  division  is  more  than  dichotomous 
(§  31),  we  have  a  series  of  disparate  terms,  exhaust- 
ive and  coexclusive ;  thus : 

bodies 


C  is  either  D,  or  E,  or  F,  or. 


soL 


liq. 


Bodies  are  solid,  or  liquid,  or  aeriform. 

Disparates,  in  logical  treatment,  must  be  reduced 
to  contradictories  by  grouping  them  into  two  op- 
posed members ;  thus : 

Bodies  are  either  solid  or  (liquid  or  aeriform =)  fluid. 
Less  than  all  the  members  of  a  disparate  series 


CONDITIONAL    PE0P0SITI0N8  151 

will  not  yield  a  disjunctive  judgment,  since  they 
are  not  exhaustive.     We  cannot  say  : 

angles 

Bodies  are  either  solid  or  aeriform.  j 

Angles  are  either  acute  or  obtuse.  |_acuto_ 


Hence  it  appears  that  contraries,  being  any  two 
members  of  a  disparate  series  (§  31),  cannot  as 
such  constitute  a  disjunctive,  for  both  may  be  false. 
"We  cannot  say,  Men  are  either  whits  or  hlack,  for 
some  are  red,  and  so  the  statement  is  neither  true 
nor  logical.  When  formal  contraries  are  affirmed 
disjunctively,  it  is  an  indirect  assertion  that  a  ter- 
tium  does  not  exist,  and  so  they  become  contra- 
dictories ;  as,  Sheep  are  either  white  or  black.  Also 
contraries  may  be  stated  disjunctively  as  mere 
alternatives ;  as.  Speak  briefly,  or  be  silent.  A  cop- 
ulative proposition,  however,  is  formed  from  con- 
traries ;  as.  Ye  cannot  serve  God  and  Mammon. 

In  logical  strictness,  disjunct  members  must  be 
not  only  exhaustive,  but  coexclusive.  Yet  we  often 
make  an  imperfect  division  wherein  the  species 
are  communicant  or  intersect,  yielding  a  specific 
disjunction  wherein  both  may  be  true.  For  ex- 
ample : 


miscbiei-maker 

Jack  is  either  a  fool  or  a  knave. 


That  is,  he  must  be  one,  he  may  be  both.  Hence 
denying  one  affirms  the  other ;  but  affirming  one, 
nothing  follows.  As  this  is  the  principle  of  sub- 
contrary  opposition,  we  distinguish  the  form  as 
subcontrary  disjunction.     The  copulative  and  this 


152  DEDUCTION 

subcontrary  proposition  are  mutually  convertible 
by  a  sort  of  contraposition ;  thus : 

Either  ye  do  not  serve  God,  or  ye  do  not  serve  Mammon. . .  .subcontrary. 
Jack  is  not  both  smart  and  good copulative. 

Disjunctive  judgments  always  affirm,  are  always 

positive,  never  negative.     In  cases  where  denial  is 

possible,  it  is  done  by  neither — nor,  thus : 

C  is  neither  D  nor  E.  character 

Tlie  boy  is  neither  smart  nor  good.  s™^""'  g°°^ 

This,  however,  is  not  a  disjunctive  proposition,  but 
a  negative  categorical  compound,  a  double  denial. 
In  Give  me  neither  poverty  nor  riches,  the  implied 
tertium  is  sought.  While  either — or  are  signs  of 
disjunction,  neither — nor  are  not  at  all  disjunctive. 

§  115.  A  disparate  series  may  be  transformed 
by  a  supposition,  thus : 

An  angle  is  either  acute,  right,  or  obtuse; 

If  an  angle  be  not  acute,  it  is  either  right  or  obtuse. 

Either  the  doctor  is  not  skilful,  or  the  patient  is  beyond  remedy, 

or  he  will  recover  ; 
If  the  doctor  be  skilful,  either  the  patient  is  beyond  remedy,  or 

he  will  recover. 

Either  A  is  not  B,  or  C  is  D,  or  C  is  non-D; 
If  A  be  B,  C  is  either  D  or  non-D. 

Such  is  the  genesis  of  the  dilemmatic  or  con- 
junctive-disjunctive proposition,  which,  as  this 
name  indicates,  is  a  compound  of  the  two  preced- 
ing forms,  and  hence  involves  no  new  principle. 
It  may  be  defined  as  a  conjunctive  having  a  dis- 
junction in  the  protasis  or  in  the  apodosis,  or  in 


CONDITIONAL    PROPOSITIONS  153 

both  ;  or,  viewed  inversely,  as  a  disjunctive  having 
a  conjunction  in  one  or  both  members. 

Usually  its  forms  are  said  to  be  numerous  and 
intricate.     But  we  hold : 

1st.  That  a  difference  in  the  matter  or  quality 
of  clauses  wherein  there  is  partial  identity  makes 
them  distinct  clauses,  having  a  distinct  formula. 

2d.  That  the  distinction  between  contradictory 
and  subcontrary  opposition  may  be  disregarded, 
understanding  that  each  formula  represents  either. 

3d.  That  trilemmatic,  tetralemmatic,  and  poly- 
lemmatic  forms  are,  for  logical  treatment,  to  be 
grouped  into  dilemmatic  contradictory  forms. 

These  points  being  allowed,  the  following  for- 
mulas are  exhaustive : 

1,  Simple,  (a)— Either  if  A  be  B,  C  is  D;  or  if  A  be  B.  E  is  F; 

— having  antecedents    identical   and   conse- 
quents disjunct.  J 
(b)— Either  if  A  be  B,  C  is  D;  or  if  E  be  F,  C  is  D;  [ 

— having   antecedents    disjunct    and    conse-' 
quents  identical. 

2,  Complex,  —Either  if  A  be  B,  C  is  D;  or  if  E  be  F,  G  is  H. 

— having    antecedents    disjunct   and   conse- 
quents disjunct. 

The  following  are  concrete  examples  of  these 
several  forms : 

1  (a) — If  Socrates  was  innocent,  Anytus  was  either  deceived  or  perjured, 

(b) — If  a  man  be  either  well  or  ill  deserving,  he  is  a  moral  agent. 
2 If  the  accused  was  deliberate,  he  was  criminal ;  or  if  not,  insane. 

§  1 16.  It  is  now  apparent  that  the  conjunctive  judg- 
ment is  the  basis  of  the  conditional  forms.  Let  us,- 
then,  inquire  more  particularly  into  its  significance. 


154  DEDUCTION 

The  conjunctive  is  sometimes  thought  as  a  quali- 
fied proposition.  For  example :  If  air  he  jpure^  it 
is  wholesome.  This  taken  from  testimony,  or  ob- 
tained by  induction  from  experience,  does  not  im- 
ply any  reasoning,  though  capable  of  being  con- 
strued syllogistically,  but  is  a  simple  judgment, 
equipollent  with  :  Pure  air  is  wholesome. 

More  generally,  however,  a  reasoning  is  implied. 
Observe  that  the  clauses  may  be  in  form  either 
positive  or  negative,  but  that  in  fact  they  are 
neither  affirmed  nor  denied.  In  If  A  is,  B  is,  it 
is  not  said  that  A  is,  or  that  B  is.  In  If  virtue  he 
Tciwwledge,  it  is  teachable,  it  is  not  said  either  that 
virtue  is  knowledge,  or  that  it  is  teachable.  The 
clauses  are  posited  not  really,  but  ideally.  Observe 
also  that  the  proposition  as  a  whole  is  always  and 
only  afiirmative.  What,  then,  is  affirmed  ?  Merely 
a  relation  between  the  members ;  not,  however, 
the  relation  of  containing  and  contained,  but  a 
relation  of  dependence,  the  relation  of  sequence. 
Yi.^.,If  A  is,  then  (or  it  follows  that)  B  is.  Or,  B 
is,  if  {or  follows  from)  A  is.  Evidently  the  prota- 
sis is  a  logical  condition  or  reason,  a  premise,  and 
the  apodosis  is  a  consequent  or  conclusion.  Sup- 
plying an  unexpressed  premise,  we  have : 
(All  knowledge  is  teachable  ;) 
If  Virtue  be  knowledge, 
then  Virtue  is  teachable Barbara, 

The  conjunctive  proposition,  therefore,  is  an  en- 
thymeme  (§  104).  Since  its  matter  is  ideally  stated, 
it  affirms  a  sequence  only ;  it  is  a  judgment  con- 


OOKDITIONAL   PKOPOSITIONS  155 

cerning  judgments,  expressing  in  the  purest  man- 
ner the  syllogistic  judgment  (§  90). 

All  the  various  forms  of  inference  are  implied  by 
conjunctive  propositions.  Immediate  inference  by 
determination  (§  80)  is  affirmed  in  If  coal  he  fuel^ 
then  cheap  coal  is  cheap  fuel;  conversion  ^er  ol- 
dens, in  If  triangles  he  figures^  then  some  figures  are 
triangles^  etc.  The  latter  exemplifies  a  conjunctive 
form  of  two  terms  only. 

Mediate  inference  is  implied  by  those  of  three  or 
more  terms.  Of  the  forms  given  in  §  112,  viewing 
them  as  ideal  enthymemes  and  supplying  the  un- 
expressed premises,  1  (a)  yields  Barbara,  or  other 
moods  of  Fig.  1 ;  1  (b)  yields  Cesare ;  1  (c)  yields 
Darapti ;  but  1  (d)  yields  Barbara,  confirming  the 
rejection  of  Fig.  4  (§  102).  The  form  2,  of  four 
terms,  yields  a  sorites,  thus : 

(Socrates  was  wise;) 
If  the  wise  be  virtuous, 
(And  the  virtuous  be  innocent,) 
then  Socrates  was  innocent. 

§  117.  Praxis.  Name  each  of  the  following  ex- 
amples in  terms  of  second  intention ;  designate  the 
section  and  paragraph  it  particularly  illustrates, 
explaining  how ;  and  then  reply  to  the  special  points 
required. 

Distinguish  the  four  following,  and  redress  as 
logical  conditions: 

1.  We  may  enter,  if  there  be  room. 

2.  If  the  moon  has  passed  the  meridian,  it  will  soon  be 

high  tide. 


156  DEDUCTION 

3.  If  the  moon  has  no  atmosphere,  it  has  no  twilight. 

4.  If  he  happened  to  be  there,  you  surely  met  him. 

Are  the  following  seven  examples  categorical  or 
conditional  ? 

5.  I  will  not  let  thee  go,  unless  thou  bless  me. 

6.  Until  the  night  comes,  we  must  work. 

7.  Is  any  among  you  afflicted  ?  let  him  pray. 

8.  Lear  is  either  at  the  hut,  or  at  the  palace. 

9.  Hiawatha  left  his  hut  or  wigwam. 

10.  It  has  not  been  decided  whether  the  war  will  con- 

tinue or  not. 

11.  Neither  flattery  nor  threats  could  prevail. 

Having  described  the  following  thirteen  exam- 
ples, reduce  disparates  to  contradictories,  also  sub- 
contraries  to  copulatives,  and  vice  versa : 

12.  They  who  slew  Caesar  are  either  patriots  or  parri- 

cides. 

13.  Either  Caesar  was  ambitious,  or  Brutus  was  criminal. 

14.  Either  if  this  be  a  judgment,  it  affirms  or  denies; 

or  if  it  be  a  question,  it  does  neither. 

15.  The  sun  moves  round  the  earth,  or  the  earth  moves 

round  the  sun. 

16.  A  woman  either  loves  or  hates  ;  she  never  thirds  it. 

17.  Punishment  is  intended  either  to  repress  crime  or  to 

reform  the  criminal. 

18.  Your  god  either  is  talking,  or  is  pursuing,  or  is  in 

a  journey,  or  peradventure  he  sleepeth.      (From 
this  obtain  a  conjunctivo-disjunctive.) 

19.  Wherever  there  is  smoke,  there  is  fire. 

20.  Whenever  the  moon  is  on  the  ecliptic,  there  is  an 

eclipse. 


CONDITIONAL    PROPOSITIONS  157 

21.  There  could  be  no  choice,  were  there  no  difference. 

22.  Day  and  night  are  never  simultaneous. 

23.  Every  man  is  already  either  justified  or  condemned. 

(  What  genus  is  here  divided?  Reduce  to  conjunc- 
tives.) 

24.  Either  my  wish  is  fulfilled,  or  you  have  disappointed 

me.     {Mediate.     Evolve,  as  in  §  113.) 

Having  designated  the  names  and  specific  forms 
of  the  following  examples,  reduce  the  conjunctivo- 
disjunctives  to  disparate  disjunctives,  and  vice  versa: 

25.  If  Caesar  live,  he  will  either  rule  or  ruin. 

26.  If  we  go  to  war,  we  must  either  contract  a  debt,  or 

increase  taxation,  or  indemnify  ourselves  at  the 
enemy's  expense. 

27.  If  my  chess-king  be  moved,  or  if  he  be  covered,  or 

if  I  capture  the  attacking  piece,  nevertheless  I 
shall  be  checkmated  at  the  next  move. 

28.  Either  if  education  be  popular,  compulsion  is  un- 

necessary ;  or  if  it  be  unpopular,  compulsion  will 
be  resisted ;  or  if  the  people  be  indifferent,  com- 
pulsion will  be  fruitless. 

29.  The  mastery  of  an  abstruse  science,  unless  there  be 

competent  instruction,  is  hardly  possible,  or  at 
best  is  imperfect. 

Complete  in  syllogistic  form  the  reasonings  im- 
plied in  the  first  four  examples  in  §  112. 
Why  must  the  consequent  in  1  (b)  be  negative  ? 
Why  must  the  consequent  in  1  (c)  be  particular  ? 


VII.— CONDITIONAL   SYLLOGISMS 

§  118.  The  various  forms  of  the  conditional  prop- 
osition are  used,  without  regard  to  their  implied 
reasoning,  as  premises  in  further  reasoning,  A  few 
illustrations  shall  suffice. 

The  following  is  Barbara,  easily  solved  by  re- 
placement (§  93) : 

;     If  the  using  of  credit  be  a  demand  for  goods,  all  forms  of  credit 
affect  prices; 
But  bills  of  exchange  are  a  form  of  credit; 
.'.  If  the  using  of  credit  be  a  demand  for  goods,  bills  of  exchange 
affect  prices. 

The  following  is  Carnestres,  from  a  disjunctive 
premise : 

All  sciences  are  either  pure,  inductive,  or  mixed; 
Astrology  is  neither; 
.'.Astrology  is  not  a  science. 

The  following,  from  a  conjunctivo-disjunctive,  is 
Barbara  with  transposed  premises  : 

If  a  ruler  make  an  entirely  unselfish  use  of  despotic  power, 

he  must  be  either  a  saint  or  a  philosopher  ; 
But  saints  and  philosophers  are  rare  ; 
.•.Those  rulers  who  so  conduct  themselves  are  rare. 

The  following  is  a  sorites  formed  of  conjunctives, 
and  resolving  into  two  syllogisms : 


CONDITIONAL    SYLLOGISMS  159 

If  the  Scriptures  be  the  word  of  God,  they  should  be  clearly 

explained ; 
If  they  should  be  clearly  explained,  they  must  be  diligently 

studied; 
If  they  must  be  diligently  studied,  an  order  of  men  must  be 

devoted  to  them; 
.'.If  the  Scriptures  be  the  word  of  God,  an  order  of  men  must 

be  devoted  to  them. 

The  foregoing  are  strictly  and  properly  condi- 
tional syllogisms,  though  this  title  has  been  usurped 
by  other  forms  (§  119  sq.).  They  may  be  distin- 
guished from  categorical  syllogisms,  but  evidently 
the  difference  is  not  essential  (§  58). 

§  119.  Early  logicians  devised  a  system  of  con- 
ditional forms,  using  the  terminology  of  the  syllo- 
gistic forms.     Of  these  there  are  four  kinds. 

The  so-called  conjunctive  syllogism  has  for  a 
major  premise  a  conjunctive  proposition,  the  minor 
premise  and  conclusion  being  the  assertion  or  de- 
nial of  the  component  clauses.  It  is  governed  by 
the  following  axioms : 

1.  Asserting  the  reason  asserts  the  conse- ' 
quent. 

2.  Denying  the  consequent  denies  the  rea- 
son. 

Biit  denying  the  reason  does  not  deny  the  conse- 
quent, and  asserting  the  consequent  does  not  assert 
the  reason^;  for  the  consequent  may  follow  from 
some  other  reason  (§  91).  If  the  protasis  be  in  fact 
a  sine  qua  non,  it  should  be  expressed  by  Only  if, 
which  is  a  compound  form. 


160  DEDUCTION 

The  double  axiom  gives  rise  to  two  so-called 
moods.  The  forms  of  the  conjunctive  syllogism 
in  these  moods  are  as  follows : 

Modus      (      If  A  be  B ;  then        C  is  D ;  )      Modus 


PoNKNS     J.      But  A  is  B ; 
{constriKtive).  {  .'.  C  is  D. 


But  C  is  not  D ;  >•     Tollkns 
.'.  A  is  not  B.  ;    (dettructive). 


If  the  people  are  industrious,  wealth  is  increasing ; 

Wealth  is  not  increasing ; 

TOLLENS. 

.■.  The  people  are  not  industrious. 


PoNENS. —     They  are  industrious ; 
.•.  Wealth  is  increasing ; 


The  sumption  affirms,  though  one  or  both  clauses 
be  negative.  It  alone  is  conditional,  the  rest  are 
categorical.  There  may  be  four  terms,  as  above ; 
all  occur  in  the  sumption.  Hence  the  subsumption 
has  no  new  term,  and  the  conclusion  may  have 
nothing  in  common  with  it. 

From  the  axioms  two  Rules  are  derived  serving 
to  guide  and  test.     They  are  as  follows : 

1.  In  Ponens  the  subsumption  and  conclusion 
must  each  agree  with  its  correspoiding  clause  in 
both  quantity  and  quality. 

2.  In  Tollens  the  subsumption  and  conclusion 
must  each  disagree  with  its  corresponding  clause  in 
both  quantity  and  quality. 

Conclusive  deviations  from  these  rules  will,  on 
inspection,  be  found  to  lack  logical  accuracy.  The 
double  disagreement  in  Tollens  is  because  logical 
denial  is  only  by  contradiction.  When  the  subject 
is  individual,  or  a  generic  total,  as  above,  its  quan- 
tity being  fixed,  contradiction  is  merely  a  change  of 
quality. 


CONDITIONAL   SYLLOGISMS. 


161 


The  following  example  illustrates  the  rules ; 

If  any  nation  prosper,  all  are  benefited ; 


Some  are  prospering; 
I'oNBNs. — or  This  one  prospers ; 
.'.AH  are  benefited. 


Some  are  not  l)eneflted  ; 
or  That  one  is  not ;         — ToLuaca 
.•.None  are  prospering. 


Negative  clauses,  one  or  both,  conform  strictly  to 
the  rules.     Thus : 

If  A  be  not  B,  then  C  is  not  D ; 


PoNENS,  asserts.— A  is  not  B; 
.•.  C  is  not  D. 


C  is  D ; — ToLLENS,  denies. 
.A  is  B. 


On  contraponing  the  sumption — that  is,  taking  the 
negative  of  each  clause  and  then  transposing  them — 
we  find  that  the  moods  are  mutually  reducible. 

In  reductio  ad  absurdum  it  is  usual  to  state  the 
argument  hypothetically ;  then  the  tollent  mood  is 
often  so  obvious  that  it  is  not  expressed ;  e.  g.,  If 
we  say  we  have  not  sinned.,  we  rniake  God  a  liar. 


§  121.  The  disjunctive  syllogism  has  for  its  ma- 
jor premise  a  disjunctive  proposition  whose  dis- 
junction is  resolved  in  the  minor  premise  and 
conclusion.  It  is  governed  by  the  axioms  of  con- 
tradiction and  excluded  middle  (§§  9,  10).  The 
disjunct  members  being  contradictory,  affirming 
one  denies  the  other,  and  vice  versa.  This  yields 
two  moods,  each  double,  thus : 


MoDtrs 

TOLLENDO 
PONENS. 


11 


C  is  either  D  or  E  (=non-D) ; 


C  is  not  D ; 
.-.CisE.' 
or 
C  is  not  E; 
.•.CisD. 


CisD; 
.C  is  not  E. 
or 

Cis  E; 
.C  is  not  D, 


Modus 

PONENDO 
ToiiLENB. 


162  DEDUCTION 

Either  all  men  are  justified,  or  some  are  condemned ; 


ToLLKNDO — Some  are  not  justified; 
PoNENDS. — .•.  Some  are  condemned. 


None  are  condemned ; 
.All  are  justified. 


All  are  justified ; — Ponendo 
.  None  are  condemned. — Tollens. 


Some  are  condemned ; 
,  Some  are  not  justified. 


Thejumption  always  affirms.  The  conclusion  has 
the  same  quantity  as  the  subsumption,  but__the 
opposite  quality. 

When  the^isjunction  is  subcontrary  (§  114),  we 
mat_proceed  in  the  ponent  moods,  but  not  in  the 
tqllent.     For  example : 

All  afflictions  are  either  punitive,  or  tentative, 
or  disciplinary; 
To.  PoKENS. —    Job's  afflictions  were  neither  punitive  nor  dis- 
ciplinary; 
.'.  They  were  tentative. 

"  David's  were  not  tentative; 

.•.  They  were  either  punitive  or  disciplinary  (per- 
haps both). 

EQSitillg„  one  snbcoTitra.ry  does  not  sublate  t.^e 
other,  for  both  may  be  true. 

A  copulative  proposition  involving  contraries 
(§  114)  yields  conclusions  in  the  tollent  mond.s^  ^nt 
not  in  thejponent.     For  example : 

Ye  cannot  serve  God  and  Mammon; 
Po.  Tollens. —    Ye  serve  Mammon ; 
.•.Ye  do  not  serve  God. 

Sublating  one  contrary  does-Jiot.  posit  the  other, 
for  both  may  be  false.  As  the  subcontrary  dis- 
junctive and  the  copulative  propositions  contra- 
pone  into  each  other,  so  likewise  these  syllogistic 
forms  are  mutually  convertible. 


CONDITIONAL   SYLLOGISMS  163 

§  121.  The  dilemmatic  proposition,  being  a  com- 
pound form  (§  115),  furnishes  a  double  process. 
Viewing  it  as  a  conjunctive,  according  to  its  first 
definition,  and  taking  the  disjunct  members  as  a 
single  clause,  we  proceed  as  in  §  119 ;  thus ; 

If  A  be  B,  either  C  is  D,  or  E  is  F  ; 

j      Neither  C  is  D,  nor         „„, ,  „„„ 
POSKNS.— But  A  isB;  |  EisF-  — Tollkns. 

.-.Either  C  is  D,or  E  is  F.  |    .^  ^^  ^^^  '^ 

If  the  apostles  taught  falsely,  they  were  either  deceivers  or  deceived. 
PoNKNS — They  did  teach  falsely ;  I      They  were  neither  de- 
/.  They  were  either  de-  |  ceivers  nor  deceived ; 

ceivers  or  deceived,     j  .*.  They  did  not  teach  falsely. 

On  the  other  hand,  viewing  it  as  a  disjunctive, 

according  to  its  second  definition,  w^e  proceed  as 

in  §  120 ;  thus : 

If  A  be  B,  either  C  is  D,  or  E  is  F; 
To.  PoNENS. —    But  C  is  not  D  ; 
.-.If  Abe  B,  EisF. 

If  Socrates  was  innocent,  Anytus  was  either  deceived  or 

perjured; 
But  Anytus  was  not  deceived ; 
.'.If  Socrates  was  innocent,  Anytus  was  perjured. 

By  denying  Anytus  was  perjured,  we  have  another 
To.  Ponens.  The  disjunct  members  being  contra- 
dictories under  the  stated  condition,  yield  also  two 
forms  in  Po.  Tollens. 

Observe  that  neither  of  these  forms  of  the  con- 
junctivo  -  disjunctive  syllogism,  though  involving 
each  a  dilemmatic  proposition,  treated  first  con- 
junctively, then  disjunctively,  is  a  dilemma. 

§  122.  The  dilemma  is  a  conditional  syllogism 


s. 


£- 


164  DEDUCTION 

having  a  double  conjunctive  premise  and  a  dis- 
junctive premise.  Either  may  be  taken  as  the 
sumption,  but  it  is  usual  to  write  the  double  con- 
junctive first.  None  of  its  propositions  is  dilem- 
matic.     It  has  three  forms,  as  follows : 

1.  Simple  constructive :  If  A  be  B,  C,  is  D ;  and  if  E  be  F,  C  is  D ; 

PoNKNS. —  But  either  A  is  B,  or  E  is  F ; 

.-.  C  is  D. 

2.  Complex  constructive :       If  A  be  B,  C  is  D  ,  and  if  E  be  F,  G  is  H; 

PoNENS. —  But  either  A  is  B,  or  E  is  F; 

/.  Either  C  is  D,  or  G  is  H. 

3.  Complex  destructive :         If  A  be  B,  C  is  D ;  and  if  E  be  F,  G  is  H ; 

ToLLENS. —  But  either  C  is  not  D,  or  G  is  not  H ; 

.".  Either  A  is  not  B,  or  E  is  not  F. 

A  single  concrete  example  from  Demosthenes  de 
Corona  must  suffice.  It  is  in  the  complex  con- 
structive form,  as  follows : 

If  ^scbines  joined  in  the  public  rejoicings,  he  is  inconsistent ; 

if  he  did  not,  he  is  unpatriotic  ; 
But  either  he  did,  or  he  did  not ; 
.•.  Either  he  is  inconsistent,  or  he  is  unpatriotic. 

The  form  of  the  sumption  in  this  example  may  be 
expressed  thus : 

If  A  be  B,  A  is  C;  and  if  A  be  not  B,  A  is  D. 
Here  the  first  term  of  each  of  the  clauses  is  the 
same,  and  the  antecedents  differ  only  by  the  nega- 
tive.    Yet  the  form  is  complex,  for  the  clauses  dif- 
fer either  in  matter  or  in  quality  (§  115). 

There  cannot  be  both  a  simple  constructive  and 
a  simple  destructive  dilemma.  Denying  the  con- 
sequents in  No.  1  gives : 

If  A  be  B,  C  is  D;  and  if  E  be  F,  0  is  D; 
But  C  is  not  D; 
.'.A  is  not  B;  and  E  is  not  F. 


,  CONDITIONAL   SYLLOGISMS  165 

This,  however,  is  merely  a  double  conjunctive  syl- 
logism in  Tollens.  The  simple  destructive  form, 
corresponding  to  No.  1,  is  : 

If  A  be  B,  C  is  D;  and  if  A  be  B,  E  is  F; 
Hut  either  C  is  not  D,  or  E  is  not  F; 
.'.A  is  not  B. 

But  this  is  merely  No.  1  contraponed,  and  then 
treated  in  Tollens.  It  is  therefore  essentially  the 
same,  and  should  not  be  enumerated  apart. 

§  123.  Let  us  briefly  inquire  into  the  nature  of 
the  forms  presented  in  the  three  foregoing  sections. 
Are  they  truly  inferences  ?  We  recall  that  deduc- 
tive inference  is  of  two  kinds,  mediate  and  imme- 
diate. In  mediate  inference  we  determine  the  rela- 
tion of  two  notions  through  a  third,  the  middle  or 
medium.  A  syllogism  is  the  formal  expression  of 
this  mediate  process,  and  hence  a  middle  term  is  its 
essential  feature.  Now,  hypothetical  or  conditional 
syllogisms,  so  called,  contain  no  middle  term.  .There- 
fore they  are  not  syllogisms,  not  expressive  of  rea- 
soning at  all.     Inspect  the  following : 

f  If  law  prevails,  our  rights  are 

Modus  J  secure  ; Major  Premise. 

PoNENS.  j       But  law  does  prevail ; Minor  Premise. 

(^  .'.  Our  rights  are  secure Conclusion. 

There  is  no  term  here  with  which  the  two  terms 
found  in  the  conclusion  are  compared  in  the  prem- 
ises. There  are  in  all  four  terms,  and  all  found  in 
the  so-called  major  premise.  The  so-called  minor 
introduces  no  new  matter,  and  has  nothing  in  com- 
mon with  the  conclusion,  as  in  a  true  syllogism 


166 


DEDUCTION 


Are  they  immediate  inferences  ?    An  immediate 

inference  from  a  given  judgment  infers  directly — 

that  is,  without  a  medium — a  different  judgment. 

Let  us  inspect  the  same  example  presented  in  a 

slightly  varied  form : 

If  Law  prevails,  then  our  rights  are  secure. 
Law  prevails,  then  our  rights  are  secure. 

Now,  here  is  an  absolute  iteration  of  thought,  stated 
first  as  supposititious,  then  as  assertorial.  The  sub- 
ject is  the  same.  The  predication  is  the  same.  The 
second  judgment,  then,  is  not  different  logically 
from  the  first,  and  therefore  this  cannot  be  an  im- 
mediate inference.  In  the  toUent  mood  and  in  the 
disjunctive  syllogism  an  immediate  inference  by 
opposition  (§  83)  is  indirectly  involved. 

These  forms  express  primarily  the  passage  of 
thought  from  the  ideal  to  the  real,  from  the  ques- 
tionable to  the  true,  some  unexpressed  ground  hav- 
ing been  discovered.  The  process  is  therefore 
metaphysical  rather  than  logical  (§  91).  Ought 
not,  then,  these  conditional  forms,  these  pseudo- 
syUogisms,  to  be  banished  from  logic  ?  By  no 
means ;  for  they  are  true,  natural,  and  very  com- 
mon modes  of  expressing  thought,  and  hence  call 
for  logical  analysis  and  treatment.  Nothing  is 
more  common  than  for  a  reasoner  at  the  outset  to 
state  hypotheticaUy  his  premise  and  conclusion. 
This  he  does  for  the  sake  of  clearness,  and  to  show 
whither  he  is  tending.     For  example : 

If  the  prisoner  was  sane,  then  he  is  responsible  for  his  act 
His  first  argument  may  be  to  show  the  necessity  of 


CONDITIONAL    SYLLOGISMS  167 

the  sequence  herein  declared.  As  accusing  counsel, 
he  next  endeavors  to  establish  this  antecedent  minor, 
perhaps  by  showing  the  deliberation  of  the  agent, 
his  consistency,  his  motives,  etc. ;  and,  it  may  be, 
he  brings  in  the  testimony  of  medical  experts. 
When  the  argument  is  complete,  he  closes  by  de- 
claring categorically : 

The  prisoner  was  sane,  therefore  he  is  responsible  for  his  act. 

Again,  many  of  these  conditional  forms  present 
exceedingly  condensed  expressions  through  which 
thought  darts  with  rapidity ;  and  unless  the  thinker 
is  familiar  with  their  analysis,  he  is  in  danger  of 
paralogism,  or  of  being  imposed  upon  by  sophism. 
On  the  other  hand,  their  condensation  gives  to  a 
just  argument  weight,  and  logical  and  rhetorical 
force.  They  should,  then,  be  discussed^ not  only  as 
subjects  of  analysis,  but  also  because  of  the  practi- 
cal advantages  resulting  from  their  close  examina- 
tion. 

It  is  clear,  however,  that  their  nomenclature 
ought  to  be  changed.  The  unfortunate  misappli- 
cation of  the  terms  syllogism^  major  and  minor 
premise,  mood,  etc.,  and  the  attempt  to  enunciate 
rules  and  methods  of  reduction  parallel  to,  but  dis- 
tinct from,  those  of  the  true  syllogism,  have  filled 
logic  for  centuries  with  confusion  and  error.  But 
so  deeply  rooted  in  logical  literature  and  so  widely 
spread  are  this  false  system  and  terminology  that 
the  needed  correction  can  be  made  only  by  the 
highest  authority. 


168  DEDUCTION 

§  124.  Praxis.  In  what  moods  are  the  follow- 
ing three  syllogistic  forms? 

1.  Every  body  is  solid,  liquid,  or  aeriform; 
Solid,  liquid,  and  aeriform  bodies  are  elastic; 

.•.Every  body  is  elastic. 

2.  Memory  is  either  circumstantial  or  philosophic; 
Also  it  is  either  voluntary  or  spontaneous; 

.•.In  this  case,  what  is  either  voluntary  or  spontaneous  is  also 
either  circumstantial  or  philosophic. 

3.  Desires  are  either  spontaneous  or  voluntary; 
But  whatever  is  voluntary  has  moral  quality; 

.•.  Desires  are  either  spontaneous,  or  they  have  moral  quality. 

Describe  each  of  the  examples  in  terms  of  second 
intention ;  redress  in  strict  form  ;  if  inaccurate,  say 
wherein ;  then  reply  to  specific  points. 

4.  Mohammed  was  either  an  enthusiast  or  an  impostor ; 
But  he  was  an  enthusiast,  and  therefore  not  an  im- 
postor.— (/s  the  disjunction  contradictory  ?) 

5.  Unless  matter  can  move  itself,  its  first  motion  must 

have  been  given  it  by  a  spiritual  being.     But  mat- 
ter cannot  move  itself ;  therefore,  etc. 

6.  If  man  cannot  make  progress  towards  perfection,  we 

must  believe  him  to  be  either  an  incapable  brute, 
or  already  divine. — [Ad  abs.) 

7.  Whether  logic  be  regarded  as  a  means  of  mental  dis- 

cipline or  as  a  practical  guide  in  reasoning,  it  ought 
to  be  studied.     But  it  is  both.     Hence — (what  ?) 

8.  The  ancients  were  in  genius  either  superior  to  the 

moderns,  or  inferior,  or  equal. — [How  many  syllo- 
gisms may  be  based  on  this  ?) 

9.  If  all  testimony  to  miracles  is  to  be  admitted,  the 


CONDITIONAL   STLLOOISM8  169 

mediaeval  legends  are  to  be  believed ;  but  they  are 

not  to  be  believed,  and  therefore  no  testimony  to 

miracles  is  to  be  admitted. 
10.  There  are  two  things  we  ought  not  to  fret  about: 

what  we  can  help,  and  what  we  cannot. — {From 

this  form  a  dilemma.) 
1\.  The  greater  angle  of  a  triangle  is  subtended  by  the 

greater  side. 

If  6  >  c,  then  B>C.  ^^ 

For  if  not,  then  either  5=  G, 

or  B<C. 
But  B  =  C  is  not  true,  for  then  b  = 

which  is  against  the  hypothesis  ; 
Nor  isB<  Ctrue,  for  then  b<c{l.,  18), 

which  also  is  against  the  hypothesis  ; 
.'.B'>C.    Q.  E.  D. — Euclid,  Book  I.,  Proposition  19. 

12.  If  the  world  existed  from  eternity,  there  would  be 

records  prior  to  the  Mosaic ;  and  if  it  were  pro- 
duced by  chance,  it  would  not  bear  marks  of  de- 
sign. But  there  are  no  records  prior  to  the  Mosaic, 
and  the  world  does  bear  marks  of  design.  .-.  The 
world  neither  existed  from  eternity,  nor  is  it  the 
work  of  chance. 

13.  A  government  cannot  be  at  the  same  time  despotic 

and  the  licenser  of  a  free  press ; 
But  the  English  government  permits  a  free  press ; 
.-.  The  English  government  is  not  despotic. 

14.  If  the  books  in  the  Alexandrine  Library  be  in  con- 

formity with  the  doctrines  of  the  Koran,  there  is  no 

need  of  them ;  if  adverse,  then  also  they  should 

be  burned. 

15.  If  pain  be  severe,  it  will  be  brief;  and  if  it  last  long, 

it  will  be  slight;  hence  it  should  be  borne  patiently. 


170  DEDUCTION 

16.  If  a  man  cannot  be  virtuous,  he  must  be  either  una- 

ble to  know  what  is  right,  or  unable  to  will  what  is 
right.  But  he  is  not  unable  to  know  what  is  right, 
for  he  is  intelligent ;  nor  unable  to  will  what  is 
right,  for  he  is  free. 

17.  We  must  either  gratify  our  vicious  propensities  or 

resist  them ;  the  former  course  will  involve  us  in 
sin  and  misery,  the  latter  requires  self-denial ;  there- 
fore we  must  either  fall  into  sin  and  misery,  or 
practise  self-denial. 


VIIL— QUANTITATIVE  FORMS 

§  125.  The  distinction  between  the  qualitative 
or  logical  whole  and  the  quantitative  or  mathe- 
matical whole  has  already  been  indicated  (§  23), 
and  some  note  made  of  the  latter  (§  24).  It  is 
now  needful  to  examine  the  quantitative  forms  of 
thought  more  particularly,  because  of  their  essen- 
tial difference,  and  because,  though  constantly  oc- 
curring, logicians  commonly  either  neglect  them 
altogether,  or  else  confound  them  with  the  co-ordi- 
nate qualitative  forms. 

In  the  qualitative  whole  the  thought  is  funda- 
mentally of  marks ;  in  the  quantitative,  of  magni- 
tudes. A  quantity,  as  distinguished  from  a  quality, 
is  measurable  by  some  standard  or  unit  of  measure, 
real  or  ideal.  Magnitudes  differ  in  kind,  and  when 
thought  as  kinds  the  notion  is  qualitative;  but 
magnitudes  of  the  same  kind  differ  in  degree,  and 
the  notion  of  degree  is  quantitative,  is  measurable, 
is  mathematical.  The  distinction  between  kind 
and  degree  is  fundamental  and  thorough-going  in 
all  thinking,  and  differentiates  the  two  wholes. 

§  126.  From  its  name  alone,  a  common  noun,  it 
is  often  impossible  to  decide  whether  a  notion  is 


172  DEDUCTION 

qualitative  or  quantitative.  Thus  mankind  in  its 
form  is  a  class,  and  the  human  race  is  a  mass,  an 
individual,  having  no  species,  and  can  be  partitioned 
only  into  sections ;  but  population  may  be  thought 
either  as  a  class  or  as  a  mass.  So  heing  or  thing  is 
a  class  including  all  kinds  of  existences,  and  the 
Universe  is  a  mass,  a  mathematical  whole,  a  col- 
lection of  all  things  into  a  unit,  the  only  one  not  a 
part  of  any  other,  and  is  capable  only  of  dissection ; 
but,  as  herein  said,  things  may  be  thought  as  a  col- 
lective whole.  Again,  animals  may  be  thought  as 
divisible  into  kinds,  or  as  the  individual  sum  total 
of  many  individuals,  severable  only,  as  the  part 
saved  in  the  ark,  and  the  part  destroyed  by  the 
deluge.  The  ambiguity  of  the  predesignations  aU 
and  some  has  been  noted  (§§  64,  QQ) ;  hence  these 
do  not  serve  to  determine  which  whole  is  thought. 
Generally,  if  not  determined  by  the  context,  it  is 
quite  ambiguous,  the  thought  readily  taking  either 
form,  and  requiring  introspection  to  ascertain  which 
of  the  two  is  thought.  So  far  of  general  names. 
Proper  names,  and  common  names  deprived  of 
their  generality  by  demonstratives,  possessives,  and 
the  like,  designate  individuals  (§  63),  and  the  thought 
is  quantitative. 

^  §  127.  Degrees  are  formally  of  two  sorts,  equal 
and  unequal.  Hence  quantitative  judgments  or 
judgments  of  degree  are  two,  both  being  mathe- 
matical comparisons. 

First,  in  the  judgment  of  equality  the  ambigu- 


QDAXTITATIVE   FORMS  173 

ous  copula  is  (§  54)  means  is  equal  to  {  =  ),  and 
when  this  is  so  expressed  the  proposition  is  unam- 
biguously quantitative.  For  example :  A  is  B ; 
The  population  of  London  is  double  that  of  New 
York  ;  X=  Y,  or  X  is  equal  to  Y,  often  expressed : 
X  and  Y  are  equal. 

Second,  the  judgment  of  inequality  conforms  to 
the  axiom,  A  whole  is  greater  than  a  part,  and  so 
has  the  copula  is  a  part  of  or  its  obverse  contains, 
or  else  is  greater  than  (>),  or  its  obverse  is  less 
than  (<).  When  these  are  expressed,  the  judg- 
ment is  unambiguously  quantitative.  For  exam- 
ple :  A  is  a  part  of  B,  ov  B  contains  A  /  Maine  is 
a  part  of  New  England,  or  conversely  ;  or  else  A 
is  greater  than  B,oy  B  <  A  •  The  earth  is  greater 
than  the  moon,  or  conversel3^  This  simple  relation 
is  often  compounded  with  other  notions ;  as  in  in- 
cluded hy,  longer  and  shorter,  better  and  worse,  strong- 
er, more  repulsive,  most  attractive,  highest,  etc.  Thus 
degrees  of  comparison  are  quantitative.  For  exam- 
ple :  Men  are  stronger  than  boys  means  The  strength 
of  men  is  greater  than  the  strength  of  boys  /  Iron  is 
not  as  heavy  as  lead  means  The  specif  c  gravity  of 
iron  is  less  than  that  of  lead  /  Zias  lies  above  coal 
means  The  height  (in  the  geological  scale)  of  Zias 
is  greater  than  that  of  coal  /  Women  love  best  means 
The  love  of  women  is  greater  than  any  other. 

In  the  qualitative  whole  an  individual  cannot 
become  a  predicate,  and  therefore  the  individual 
proposition  is  inconvertible  (§§  54,  82).  In  the 
quantitative  whole  an  individual  is  often  the  pred- 


174  DEDUCTION 

icate,  and  all  quantitative  propositions  are  always 
and  only  simply  convertible,  the  copula  in  the  sec- 
ond class  being  changed  to  its  obverse. 

When  the  predicate  is  an  individual,  or  when  it 
is  qualified  numerically  or  by  some  term  of  meas- 
ure, or  when  it  is  quantified  as  all  or  some,  directly 
or  indirectly  (§  74),  the  proposition  is  quantitative. 
E.  g.,  Aristotle  is  the  father  of  logic  j  Thou  art  the 
mam,  ^  This  is  our  ho7ne  ^  A  legion  is  {=)  ten  co- 
horts /  His  reasons  are  as  two  grains  of  wheat  hid 
in  two  bushels  of  chaffs  It  weighs  a  pound  f  All 
men  are  all  reasoners ;  Here  only  thieves  (generic 
total,  not  every  one)  a/re  to  he  dreaded^  or  all  (the 
sum  total)  that  is  to  he  dreaded ;  The  committee 
(collective)  consists  of  some  (a  portion  or  section) 
of  our  wisest  men  /  The  population  of  London  is 
more  than  {>)  a  million.  Generally  the  character 
of  the  predicate  determines  in  w^hich  whole  the 
proposition  lies. 

The  complete  generality  of  many  quantitative 
forms  should  be  observed.  Several  of  the  fore- 
going examples  are  cases.  Pure  mathematics,  the 
science  of  quantity,  treats  almost  exclusively  of 
such  abstract  generalities;  as  6=2x3-,  o?—y'= 
{x  +  y)  (x—y);  Triangles  on  the  same  hase,  and  be- 
tween the  sa/me  parallels,  a/re  equal. 

^  §  128,  Inference  in  the  quantitative  whole  is  im- 
mediate and  mediate.  Immediate  inference  from 
equivalent  propositions  conforms  to  the  Canon: 
Equals  affected  by  equals  are  equal.    This  is 


QUANTITATIVE    F0KM8  175 

a  general  statement  of  four  of  the  logical  axioms 
{KotvaX  ivvoiai)  of  Euclid,  that  if  equals  be  added 
to,  or  taken  from,  or  multiplied  by,  or  divided  by 
equals,  the  results  are  equal.  The  process  corre- 
sponds to  Determination  (§  80).  E.  g..  As  from  A 
horse  is  an  animal,  and  What  is  young  is  strong, 
we  may  immediately  infer  that  A  young  horse  is  a 
strong  animal,  so  from  a=:b,  and  c=d,  we  may  im- 
mediately infer  that  a  +  c—l-\-d.  The  principle, 
in  a  modified  form,  applies  to  propositions  of  ine- 
quality.    E.  g..  If  a>b,  then  2a>^h. 

§  129.  Mediate  inference  from  equivalent  propo- 
sitions conforms  to  the  Canon:  Quantities  equal 
to  the  same  thing  are  equal  to  each  other. 
This  is  Euclid's  first  logical  axiom.  The  general 
formula  is : 

If  A  =  B ;  A  t«  not  equal  to  B ; 

and  B  =  C ;  Negatively :    B  is  equal  to  C ; 

then  A  =  C.  .'.Aw  not  equal  to  C. 

This  may  be  called  the  syllogism  of  equivalence.,. 
Obviously  it  is  a  specific  application  of  the  Primary 
Law  of  Identity  (§  8),  which  is  the  ultimate  prin- 
ciple involved  in  both  the  foregoing  canons.  The 
first  clause  of  the  canon  of  replacement  (§  93)  also 
justifies  the  process,  and  is  even  more  general.  A 
concrete  example  in  this  form  is  as  follows : 

The  density  of  the  human  body  is  the  density  of  water; 
The  density  of  water  is  the  density  of  air  taken  817  times; 
.'.The  density  of  the  human  body  is  817  times  the  density  of  air. 

It  will  be  observed  that  the  middle  term  here  is 


176  DEDUCTION 

a  standard  of  measure.  And  this  gives  occasion  to 
remark  the  logical  function  of  standards  of  meas- 
ure of  all  sorts.  They  furnish  the  media  through 
which  we  are  enabled  to  compare  quantities  which 
cannot  be  immediately  compared.  The  yard,  the 
bushel,  the  pound,  the  atomic  weight  of  hydrogen, 
the  thermometer,  barometer,  electrometer,  etc.,  sup- 
ply us  with  middle  terms  through  which  to  reason 
in  our  calculations.  The  metric  system  furnishes  a 
common  middle  term,  the  metre,  by  which  to  com- 
pare its  various  standards  with  each  other. 

In  the  syllogism  of  equivalence  the  order  of  prem- 
ises is  obviously  indifferent.  The  order  of  subject 
and  predicate  is  also  indifferent ;  that  is,  either  term 
may  be  made  the  subject  of  thought,  and  the  other 
the  predicate,  without  other  change.  The  distinc- 
tion of  major  and  minor  terms,  and  consequently 
that  of  major  and  minor  premises,  does  not  exist, 
the  terms  being  equivalent.-  The  equivalent  prop- 
osition is  always  and  only  simply  convertible.  The 
doctrine  of  Conversion,  then,  has  no  place  relative 
to  this  syllogism.  It  follows,  also,  that  Figure  is 
of  no  moment,  and  is  to  be  disregarded.  Moods 
are  reduced  to  two,  the  positive  and  the  negative ; 
for  the  quantification  of  every  term  is  always  total. 
Hence  questions  concerning  distribution  and  non- 
distribution  cannot  arise. 

These  eliminations  render  the  logical  treatment 
of  this  syllogism  exceedingly  simple.  Perhaps  from 
this  simplicity  it  is,  as  well  as  from  its  clear  intui- 
tive exactness,  that  elementary  mathematics  is  with- 


QUANTITATIVE    FOBMS  177 

in  the  grasp  of  immature  minds,  even  children 
often  being  able  to  apprehend  it  quite  thoroughly; 
whereas  reasoning  in  the  logical  whole,  with  the 
qualitative  syllogism  as  the  unit  form,  requires 
more  mental  discipline  and  maturity. 

§  130.  A  geometrical  example  (Euclid,  I.,  32)  con- 
forming to  the  canon  of  mediate  inference  may  be 
stated  as  follows : 

The  three  interior  angles  of  a  triangle  are  equal  to  two  right 

angles; 
For  the  interior  angles  are  equal  to  the  adjacent  exterior  and 

interior  angles; 
And  these  are  equal  to  two  right  angles. 

The  expression  is  rendered  more  facile  by  the  use 
of  a  lettered  figure,  the  letters  taking  the  place  of 
a  verbal  description  of  a  part ;  but  the  processes  are 
identical. 

Let  us  exhibit  a  slightly  varied  and  redressed 
proof  of  the  same  proposition  by  aid  of  a  lettered 
figure;  thus: 

Through  the  apex  of  an  angle  b  draw  h  line  parallel  to 
the  opposite  side.     Then : 

a=a'. Prop.  29. 

b=b Identit}'. 

c=c' Prop.  29. 

a  +b+c  =a'+b  +  c'. Canon  of  immediate  inference. 

a'+b+c'=2L Prop.  13. 

.'.8  +b+c  =2  L Canon  of  mediate  inference. 

This  last  equation  may  of  course  be  translated  into 
words. 

f.  It  is  needful  to  remark  particularly  that  whether 
the  proposition  be  expressed  in  symbols  or  in  words, 
12 


178  DEDUCTION 

both  have  the  same,  and  indeed  a  complete,  gener- 
ality. Also  that  the  passing  from  one  to  the  other 
is  not  at  all  a  logical  process,  but  simply  a  trans- 
lation of  expression.  Changing  the  symbols  into 
words  is  often  spoken  of  as  a  generalization  or  an 
induction,  but  it  is  neither.  Nor  is  the  reverse  a 
deduction ;  yet  the  following,  for  instance,  is  some- 
times laid  down  as  a  syllogism : 

/T^N.  All  radii  of  a  circle  are  equal ; 

[  ^y j^         AC  and  BC  are  radii  of  a  circle; 

\v         y         /.AC  and  BC  are  equal. 

But  there  is  here  no  progress  of  thought,  no  change 
of  thought  whatever,  only  of  expression.  AC  and 
BC  stand  for  any  radii  of  any  circle;  hence  the 
simulated  conclusion  is  as  completely  general  as 
the  verbal  proposition  which  simulates  a  major 
premise,  and  nothing  whatever  is  proved. 

§  131.  Mediate  inference  from  propositions  of 
inequality  conform  to  Euclid's  9th  logical  axiom, 
A  whole  is  greater  than  a  part.  This,  modified, 
furnishes  the  Canon  :  A  part  of  a  part  is  part 
of  the  ■whole  (§  93),  Syllogisms  in  conformity 
with  this  canon  may  be  called  partitive  syllogisms. 
A  single  example,  and  the  converse  form,  shall  suf- 
fice for  illustration : 

A  minute  is  apart  oj  a  degree;  A  contains  B; 

A  degree  is  a  part  qfn  circle ;       Converse :     B  contains  C ; 

.*. A  minute  is  a  part  o/'a  circle.  .'.A  contains  C. 


QUANTITATIVE    FORMS  179 

Another  modification  of  the  axiom  furnishes  the 
Canon:  A  greater  than  a  greater  is  greater 
still  than  the  thing.  Syllogisms  conforming  to 
this  canon  may  be  called  comparative  syllogisms. 
The  formula  is : 

A>B;  B  U  less  than  A;         A 

B>C;         Conversely:      Cis  less  than  B ;  B 

.*. A >  C.  .-.Cm  less  than  A.  C 


E.  g The  planet  Jupiter  is  greater  than  the- earth; 

The  earth  w  greater  than  the  moon ; 
.'.The  planet  Jupiter  is  greater  tJian  the  moon. 

Logicians  sometimes  distinguish  between  the  in- 
ferences a  minor e  ad  majus  and  a  majore  ad  minus; 
but  the  distinction  is  superficial,  since  one  is  sim- 
ply convertible  into  the  other. 

Observe  that  the  premises  authorize  a  pregnant 
conclusion,  one  a  fortiori  (§  108),  usually  expressed 
thus: 

.'.By  BO  much  the  more  is  A  greater  than  C;  or: 

.'.C  is  still  lest  than  A;  or: 

.'.A  fortiori  the  planet  Jupiter  is  greater  than  the  moon. 

The  following  example  is  followed  by  its  re- 
dressed form : 

The  tree  is  higher  than  the  man; 
The  spire  is  higher  than  the  tree; 
.'.The  spire  is  still  higher  than  the  man. 

The  height  of  the  tree  is  greater  than  the  height  of  the  man; 
The  height  of  the  spire  ts  greater  than  the  height  of  the  tree; 
.'.  The  height  of  the  spire  is  still  greater  than  that  of* the  man. 

The  following  (Euclid,  I.,  20,  redressed)  exhibits 
a  variation  in  respect  of  its  symbolic  statement ; 


180  DEDUCTION 

Any  two  sides  of  a  triangle  are  greater  than  the  third. 

Extend  the  side  A  until  C'=C.     Then: 

c'=c Prop.  5. 

5  '"*■/  »  +  c'>c' Ax.  9. 

A ^-''■""^^^K  .'.a  +  c'>c Mediate  inference. 

^\c-        Then  A  +  C'>B Pro'p.  19. 

-^ '~^  A  +  C'=A  +  C....Ax.2. 

.■.A  +  C  >B Mediate  inference. 

Not  only  do  both  kinds  of  judgments  of  degree 

occur  in  the  same  reasoning,  as  in  the  foregoing 

demonstration,  but  qualitative  judgments  also  often 

combine  with  quantitative.     For  example : 

Regulus  is  a  star  of  the  first  magnitude; 
Sirius  is  as  bright  or  brighter  than  Regulus; 
.'.Sirlus  is  a  star  of  the  first  magnitude. 

A  proposition  whose  terms  are  not  merely  equiv- 
alent, but  in  strict  and  entire  identity  (§  8),  that  is, 
in  what  has  been  called  the  sibi-relation,  cannot 
serve  as  a  premise  in  a  proper  syllogism ;  for  such 
terms,  differing  merely  as  to  words,  are  one  in 
thought,  and  consequently  we  should  have  a  pseudo- 
syllogism  of  only  two  terms,  begging  the  question 
(§  146).     Cf.  §  26 ;  §  95,  Ex.  12 ;  and  §  130. 

Quantitative  relations  may  be  expressed  also  in 
the  several  forms  of  the  so-called  conditional  syl- 
logism.    For  an  instance,  see  §  124,  Ex.  11. 

§  132.  Praxis.  State  whether  the  following  prop- 
ositions are  qualitative  or  quantitative.  If  the  lat- 
ter, redress  with  the  copula : 

1.  It  is  the  duty  of  every  man  to  serve  God  and  honor 
the  king.     Only  birds  are  feathered. 


cm  I       \   _ 

QUANTITATIVE    FORMS  181 

2.  George  Eliot  is  Mrs.  Lewes.      Arrows  are  swifter 

than  eagles. 

3.  God  alone  is  good.     We  are  all  sinners. 

4.  Every  sly  act  is  nothing  less  than  dishonest. 

6.  The  container  contains  the  contained.     That  man 
is  my  father. 

6.  None  but  Aryans  are  capable  of  the  highest  civil- 

ization. 

Can  the  deduced  formula  Circ—^TtR,  or  this 
vis  viva  — mY*,  be  generalized? 

Name  the  class  to  which  each  of  the  following 
reasonings  belongs.  Supply  any  lacking  proposi- 
tion. Kedress,  if  need  be,  exhibiting  the  copulas. 
Construe  the  first  as  qualitative  also : 

7.  Wisdom  is  more  precious  than  rubies,  and  rubies 

than  gold ;  hence  wisdom  is  of  yet  higher  value 
than  gold. 

8.  The   author  of  Athalie  was   the   greatest  French 

dramatist ;  7  ^^~^ 

But  Racine  was  the  author  of  Athalie. 

9.  The  market  value  of  my  cloke  is  $15; 

A  sword  will  cost  me  $10.     (Luke  xxii.  36.) 

10.  John  knew  more  than  Peter,  and  Peter  than  Mark; 

.'.  John  knew  more  than  Mark.  Vj 

11.  Aristotle  lived  after  Plato,  and  Plato  after  Socrates; 
/.  Aristotle  lived  after  Socrates.  \j 

12.  Virginia  is  one  of  the  Southern  States ; 

The  Southern  States  are  a  part  of  the  Union ;     ,  \ 
.'.  Virginia  is  a  part  of  the  Union. 

13.  Lias  lies  above  Red  Sandstone ; 
Red  Sandstone  lies  above  Coal ; 

,*.  Lias  lies  above  Coal. 


182  DEDUCTION 

14.  The  orbit  of  Venus  is  within  that  of  the  Earth : 

And  this  within  that  of  Jupiter;  -'T 

.-.  The  orbit  of  Venus  is  within  that  of  Jupiter. 

15.  The  dome  is  under  the  sky,  and  the  altar  under  the 

dome  ;  therefore  the  altar  is  under  the  sky.  '^/t 

16.  Behold,  the  heaven  and  heaven  of  heavens  cannot 

contain  thee;  how  much  less  this  house  that  I 
have  builded !     ~  " 

17.  It  were  better  to  have  no  opinion  of  God  at  all  than 

such  an  opinion  as  is  unworthy  of  him  ;  for  the 
one  is  unbelief,  the  other  is  contumely  ;  and  cer- 
tainly superstition  is  the  reproach  of  the  Deity. 

Prove  the  following  proposition  (Euclid,  I.,  15), 
first  in  words  only,  then  by  the  figures  and  letters, 
as  in  §  130 : 

18.  If  two  straight  lines  intersect, 

the  vertical  angles  are  equal. 

Kedress  the  following  demonstration  (Euclid,  I., 
18)  as  in  §  131 : 

19.  The  greater  angle  of  a  tri- 

angle   is    opposite    the 
greater  side.  B^ 

Let  A  C  be  greater  than  A  B  ;  take  A  D  equal  to  A  B, 

and  join  B  D. 
Then  since  ADB  is  the  exterior  angle  of  the  triangle 

B  D  C,  it  is  greater  than  the  interior  opposite  angle 

D  C  B.— Prop.  16. 
But  since  the  side  A  D  is  equal  to  the  side  A  B,  the  angle 

A  D  B  is  equal  to  the  angle  A  B  D. — Prop.  5. 
Therefore  the  angle  A  B  D  also  is  greater  than  the  angle 

ACB. 
Much  more  then  is  the  angle  ABC  greater  than  the  angle 

ACB.— Ax.  9.     Q.  K.  D. 


IX.— FALLACIES 

§  133.  Anj  violation  of  logica]  law  is  a  jallaqy. 
Logical  forms  are  determined  originally  by  the 
nature  of  intellect  as  expressed  in  the  primary  laws 
of  thought,  from  which  are  derived  by  deduction 
the  laws  of  special  forms.  Hence  any  essential  de- 
viation from  a  form  is  a  violation  of  its  law,  and  so 
a  fallacy.  Under  this  wide  definition  come  illog- 
ical predications,  generalizations,  definitions^  divi-l 
sionSj  etc.,  as  well  as  illogical  inferences^  '^ 

Two  remarks  are  needful.  First,  that  logical 
forms,  though  necessary,  as  stated  in  the  definition 
of  logic  (§  l),_are  nevertheless  violable  (§  5).  They 
are  necessary  to  knowledge  of  truth,  and  cannot  be 
violated  without  risk  of  error,  folly,  falsity ;  just 
as  a  violation  of  the  laws  of  health  risks  disorder, 
disease,  death.  Second,  that  what  does  not  violate 
logical  law,  however  false  in  matter,  is  not  fallacy. 
Our  science  does  not  take  into  consideration  the 
material  truth  or  falsity  of  judgments  (§§  4,  50). 
Therefore,  in  case  of  inference,  the  truth  or  falsity 
of  the  premises  and  conclusion  is  disregarded,  the 
ftrm  alone  being  considered  (§  91).  Many  logi- 
cians, overlooking  this,  include  among  fallacies  syl- 
logisms correct  in  form,  but  having  false  premises. 


184  DBDucnow 

These,  however,  are  not  fallacies.  For  example,  if 
some  one  argues  from  the  distress  of  a  country 
that  the  government  is  tyrannical,  we  must  sup- 
pose him  to  assume  that  Every  distressed  country 
is  under  tyra/rmy,  which,  though  false,  leads  logi- 
cally to  his  conciasion,  and  there  is  no  fallacy ;  or 
that  Every  country  under  a  tyranny  is  distressed^ 
which  may  be  true,  but  the  inference  from  this, 
the  middle  being  undistributed,  is  a  non  sequitur, 
a  fallacy. 
The  distribution  of  fallacies  is  as  follows : 

{Paralogisms 
«     ,.  i  In  diction. 

Sophisms      \  ^    "i^"""- 
(  In  matter. 

The  differences-  here  indicated  wiU  be  explained  in 
the  progress  of  the  discussion. 

§  134.  A  paralogism  is  a  violation  of  a  law  of 
form,'  msinifest'  without  regard  to  the  diction  or 
matter!  DTlliis  we  have  already  had  many  inci- 
dental examples.  When  the  form  of  a  proposition 
is  obviously  the  logical  paradox,  A=non-A,  as  To 
do  wrong  is  sometimes  right ;  or  when  there  is  an 
inference  from  All  A  is  B,  to  All  B  is  A,  as  To 
possess  a  large  amount  of  money  is  to  he  wealthy^ 
hence  To  he  wealthy  is  to  possess  a  large  amount  of 
money ;  or  an  inference  through  an  undistributed 
middle ;  or  an  inference  involving  the  ilhcit  proc- 
ess— these  and  the  like  are  paralogisms. 

Sometimes,  however,  law  is  only  apparently,  not 
really,  violated.     For  example : 


FALLACIES  185 

No  rose  is  without  thorns; 
This  bouquet  is  ef  roses ; 
/.This  bouquet  has  thorns. 

Here  seems  to  be  an  affirmative  conclusion  from 
a^negative  premise,  violating  General  Kule  4.  But 
on  looking  into  the  diction  of  the  major  premise, 
it  is  seen  to  yield  by  infinitation  Every  rose  has 
thorns,  and  then  the  form  is  Barbara. 

§  135.  Sophisms  in  diction,  in  voce,  are  such  as 
require  an  inspection  of  the  expression  in  order  to 
detect  the  formal  fault.  They  all  arise  from  am- 
biguities of  language.  A  term  repeated  ambigu- 
ously, though  identical  to  eye  and  ear,  must  be 
counted  twice,  for  it  represents  two  notions.  A 
syllogism  containing  such  a  term  is  therefore,  in 
thought,  quaternio  terminerum,  a  quaternion,  a  log- 
ical quadruped  (§  94).  This  is  the  common  vice 
of  sophisms  in  diction.  Aristotle  distinguishes  six 
species,  which  we  proceed  to  examine. 

§  136.  iEquivocatio  isjhe  use  of  a  term  in  two 
different  senses.  If  it  be  the  middle  term,  it  is 
called  the  fallacy  of  ambiguous  middle,  as  in : 

Designing  persons  are  untrustworthy; 
Everybody  forms  designs ; 
.'.  Nobody  can  be  trusted. 

Likewise  an  ambiguous  major  or  minor  term  pro- 
duces a  quaternion. 

Perhaps  no  fallacy  is  so  prolific  as  this.  Living 
languages  abound  in  ambiguities,  and  no  procedure 


186    z^P  ^  /y   ^^  V  DBBUcmo:^ 

is  safe  that  does  not  keep  close  watch  upon  them. 

^  Many  important  words,  as  nature,  stute,  representa- 

tion, moral,  inconcewahle,  and  even  money,  are  quite 
ambiguous.  There  are  at  least  five  distinct  senses 
in  which  the  word  law  is  habitually  used.  The 
only  security  is  in  exact  definition  and  consistent 
usage.  As  by  attrition  crystals  become  pebbles, 
so  words  in  common  use  lose  their  sharp  meaning. 
Like  coins  defaced  by  much  handling,  current  words 
are  no  longer  clear.  Science,  to  be  accurate,  takes 
refuge  in  a  barbarous  terminology. 

_  ^  The  paranomasia  or  pun  is  the  sophism  of  equiv- 
ocation.  Here  is  a  time -honored  example:  Two 
men  ate  oysters  for  a  wager  ^  one  ate  ninety-nine,  hut 

— '  the  other  ate  two  more,  for  he  ate  a  hundred  and 

won.  This  affords  occasion  for  the  general  obser- 
vation that  jests  are  usually  mock  logic,  and  often 
in  absurd  form  let  fly  a  sharp  dart  of  truth.  The 
"  bull "  is  a  palpable  self-contradiction,  generally 
an  unconscious  blunder,  but  sometimes  on  purpose ; 
as,  Do  you  believe  in  ghosts  f  No  indeed,  I've  seen, 
too  many  of  them  '  or,  as  when  my  wife  said  to  me, 
/  hope  I  shall  not  live  to  see  you  a  frisky  widower. 

§  13T.  ^Amphibolia  differs  from  equivocation 
in  that  the  ambiguity  is  in  the  construction  of  a 
sentence  rather  than  in  a  term.  Examples  of  am- 
phiboly are :  How  much  is  twice  two  and  three  f 
I  will  go  amd  return  to-morrow.  See  Quince's  pro-j 
logue  in  Midsummer- Night'' s  Dream,  act  v.,  sc.  i.  1 
In  the  Nicene  Creed,  the   words  "by  wh©m  aH 


FALLACIES  187 

things  were  made"  are  grammatically  referable 
either  to  the  Father  or  to  the  Son.  Amphiboly 
was  the  trick  of  the  oracles.  Thus  the  prophecy 
of  the  Spirit  in  Henry  VI.,  pt.  ii.,  act  i.,  sc.  iv. : 

The  duke  yet  lives  that  Henry  shall  depose, 
But  him  outlive,  and  die  a  violent  death. 

But  this,  says  York,  is  just  the  response  of  the  ora- 
cle to  Pyrrhus : 

Aio  te,  jEacida,  Romanos  vincere  posse; 
Ibis  redibis  nuuquam  in  bello  peribis. 

§  138.  Compositio  et  divisio  are  conjoining 
what  should  be  disjoined,  and  disjoining  what 
should  be  conjoined.  Thus,  He  well  knows  the  al- 
phabet he  had  to  learn  /  In  some  things  we  offend  all ; 
Moses  was  the  daughter  of  Pharaoh's  son  •  Paul 
returned  to  his  master  one  Simus  (Onesimus).  Aris- 
totle's example  of  composition  is :  A  man  sitting 
can  walk  (i.  e.,  can  walk  sitting) ;  of  division,  he 
gives :  5  is  2  and  3,  hoth  even  and  odd.  He  treats 
them  as  distinct  species,  which  seems  unnecessary, 
since  the  distinction  between  them  generally  de- 
pends merely  on  which  of  the  propositions,  involved 
in  the  ambiguous  statement,  is  granted,  the  affir- 
mation of  the  other  being  the  fallacy.  "Whately 
construes  the  above  as  F.  Compositionis,  thus : 

Two  and  three  (diatributively)  are  even  and  odd; 
Two  and  three  {collectively)  are  five;  ' 

.•.Five  is  even  and  odd. 

This  is  clear  and  correct,  although  it  transposes 
the  titles. 


188  DEDUCTION 

The  distinction  between  fallacies  of  this  class 
and  amphibolia  is  not  altogether  clear.  In  many 
cases  we  hesitate.  Perhaps  to  either  may  be  re- 
ferred ambiguities  wrongly  resolved  by  punctua- 
tion. A  notable  example  is  found  in  the  Uuited 
States  Constitution,  Art.  1,  §  8.  After  the  word 
"  excises  "  a  semicolon  is  frequently  printed,  where- 
as in  the  original  draft,  and  in  the  authorized  edi- 
tion of  March  3,  1877,  it  is  followed  by  a  comma. 
Alexander  Hamilton  held  that  the  items  of  the  rest 
of  the  section  are  additional  powers ;  Madison,  that 
they  are  limitations.  The  semicolon  enlarges  fed- 
eral authority  ;  the  comma  favors  state-rights. 

This  gives  occasion  for  the  general  observation 
that  it  should  not  be  inferred  from  the  trifling 
character  of  many  of  the  examples  used  to  iUus- 
trate  fallacies,  that  the  fallacies  themselves  are  un- 
important. In  a  brief  trifle  a  point  is  often  clearly 
exposed  which,  lurking  in  a  body  of  weighty  mat- 
ters, may  be  fatal. 

§  139.  Accentus,  prosodia,  resolves  an  ambi- 
guity by  a  stress  of  voice  so  as  to  mislead,  gen- 
erally by  an  implication.  The  early  rabbis  laid 
emphasis  on  the  word  neighbor  in  Thou  shalt  love 
thy  neighbor  (Lev.  xix.  18) ;  hence  their  gloss,  and 
hate  thine  enemy  (corrected  in  Matt.  v.  43  sq.).  By 
emphasis  on  against  in  the  ninth  commandment, 
it  is  implied  that  one  may  bear  false  witness  in 
favor  of  another,  which  was  Jeanie  Deans's  temp- 
tation.    The  phrase  If  you  were'  hra/oe  differs  from 


^G 


FALLACIES  189 

If  you  were  hra/oe'.  So  also  Not  the  least  difference 
may  mean  no  difference  at  all,  or  by  varying  the 
stress,  a  very  considerable,  perhaps  the  greatest 
difference.  Some  words,  ambiguous  to  the  eye, 
are  resolved  by  accent,  as  to  con'jure^  to  practise 
magic,  and  to  conjure',  to  entreat  earnestly.  Mere- 
ly the  tone  may  make  all  the  difference  between 
truth  and  falsehood. 

Sarcasm  is  generally  indicated  by  the  circumflex 
accent,  and  unless  this  or  certain  tones  are  used, 
the  meaning  is  perverted ;  as.  It  cannot  he  that  a 
prophet  perish  out  of  Jerusalem.  For  other  exam- 
ples of  divine  irony,  see  1  Kings  xviii.  27 ;  Job  xii. 
2 ;  Psa.  ii.  10 ;  2  Cor.  xii.  13. 

§  140.  Figura  dictionis  occurs  when  a  meta- 
phor or  other  figure  of  speech  is  construed  liter- 
ally, or  vice  versa,  as : 

A  fox  is  a  quadruped; 

Herod  is  a  fox;  " >  ^    (^^     _,„,___^ 

.'.Herod  is  a  quadruped. 

This  seems  very  trifling.  But  let  it  be  observed 
that  figurative  expressions  abound,  that  new  mat- 
ter can  hardly  be  spoken  of  except  metaphorically, 
that  the  history  of  the  mental  sciences  shows  how 
diflBcult  it  is  to  avoid  being  misled  by  material  con- 
ceptions which  are  only  remotely  comparative,  and 
that  in  debate  illustrations  are  constantly  mistaken 
for  arguments,  and  often  are  more  convincing  than 
good  logic.  These  considerations  make  it  evident 
that  this  is  a  very  subtile  and  ruinous  form  of  fal- 


190       •  DKDUCJnON 

lacy.  Hamilton  speaks  of  it  with  great  contempt, 
unaware  that  his  famous  argument  for  immediate 
perception  is  invalidated  by  this  very  sophism. 

It  is  usual  to  include  in  this  class  errors  arising 
from  solecisms ;  as,  George  Eliot  deserves  his  fame. 
Also  those  from  paronyms ;  as,  Being  touched  with 
pity,  his  hehavior  was pit'iful  •  Ajphenomenon  is  that 
which  appears,  and  therefore  is  merely  apparent. 

§  141.  Sophisms  in  matter,  in  re^  are  such  as  re- 
quire an  inspection  of  the  matter  in  order  to  detect 
the  formal  fault.  They  are  quite  commonly  called 
"  material  fallacies,"  and  described  as  those  whose 
fault  is  not  in  form  or  diction,  but  in  matter,  mean- 
ing that  the  form  is  correct,  but  the  matter,  espe- 
cially the  premised  matter,  is  false.  If  so,  they, 
being  logically  faultless,  are  not  fallacies  (§  133). 
But  not  so,  for  these  sophisms  are  logically,  for- 
mally faulty,  onl}'  it  is  requisite  to  look  beyond  the 
diction  and  examine  the  matter  in  order  to  discover 
the  fault.  Of  this  genus  Aristotle  distinguishes 
seven  species,  which  we  proceed  to  examine. 

§  142.  Accidens  arises  from  equating  subject 
and  accident,  or  whenever  it  is  assumed  that  sub- 
ject and  accident  have  all  their  attributes  in  com- 
mon. By  accident  here  is  meant  any  subordinate 
part  of  a  general  notion,  as  in  conversion  j9<?r  acci- 
dens (§  82),  For  example  :  Men  (subject)  are  hipeds' 
Birds  are  (an  accident  of)  'bipeds ;  hence  (equating 
subject  and  accident),  Men  are  hirds,  or  Birds  are 


FALLACIES  191 

men.  But  it  is  fallaciously  assumed  that  men  and 
birds  have  all  other  attributes  in  common.  Obvi- 
ously undistributed  middle.  Again :  Since  Coriscus 
is  not  Socrates,  and  Socrates  is  a  man,  it  does  not 
follow  that  Coriscus  is  not  a  man,  because  Socrates, 
who  is  denied  of  Coriscus,  is  merely  an  accident 
of  man.     Obviously  illicit  major.     Again : 

The  Greeks  produced  masterpieces  of  art; 
The  Spartans  were  Greeks ; 
.'.The  Spartans  produced  masterpieces  of  art 

Here  the  Greeks,  the  subject  in  the  major  premise, 
is  the  name  of  a  genus  taken  as  an  undivided  whole 
(§  63),  of  which  the  Spartans  is  merely  an  acci- 
dent. It  is  fallaciously  assumed  that  whatever  is 
attributable  to  the  genus  as  such,  may  be  attributed 
to  an  accidental  member.  Obviously  ambiguous 
middle,  and  hence  a  quarternion. 

§  143.  Secundum  quid  occurs  in  an  inference 
a  dicto  secundum  quid  ad  dictum  simpliciter,  and 
vice  versa.  It  is  the  confusion  of  an  absolute  state- 
ment with  one  limited  by  time,  manner,  or  some 
accidental  relation. 

The  first  infers  from  a  statement  made  under  an 
unessential  restriction  {secundum  quid)  to  one  made 
without  restriction  {simpliciter). 

Whatever  is  pernicious  ought  to  be  forbidden; 
The  use  of  wine  is  pernicious; 
.'.The  use  of  wine  ought  to  be  forbidden. 

Here  the  minor  premise  refers  to  wine  used  im- 
moderately ;  the  conclusion,  to  wine  however  used. 


192  DEDUCTION 

This  is  the  time-honored  sophism  of  arguing  againgt 
a  thing  from  the  abuse  of  it. 

The  second  infers  from  a  statement  made  with- 
out limitation  to  one  limited,  proceeding  from  what 
is  essential  to  what  is  accidental. 

The  meat  you  bought  yesterday  you  ate  to-day ; 
You  bought  raw  meat  yesterday; 
.*.  You  ate  raw  meat  to-day. 

Here  is  inferred,  in  the  conclusion,  of  meat  with 
the  accidental  quality  of  rawness  added,  what  in 
the  major  is  said  of  it  simpl}^  that  is,  of  the  essen- 
tial substance,  regardless  of  accidental  qualities. 

The  first  of  these  cases,  when  we  look  into  the 
matter,  may  evidently  be  construed  as  illicit  minor ; 
for  what  is  premised  of  some,  a  certain  use  of  wine, 
is  concluded  of  all  use  of  wine.  The  second  case 
is  plainly  a  quaternion,  having  an  ambiguous  mid- 
dle ;  for  The  meat  you  bought  yesterday  is  used  in 
two  different  senses  —  first,  simply  or  essentially 
only ;  secondly,  with  its  accident. 

§  144.  Ignoratio  elenchi  is  ignoring  the  refu- 
tation, answering  to  the  wrong  point,  proving  some- 
thing not  the  contradictory  {elenchus)  of  the  thesis 
which  one  intends  to  overthrow.  This  supposes  a 
disputant,  an  attempt  at  confutation.  It  is  usual 
to  take  a  wider  view,  and,  under  the  title  of  Irrel- 
evant Conclusion,  or  mistaking  the  issue,  to  include 
all  cases  where  the  attempt  js_to^  establish  a  thesis 
by  a  proof  of  something  not  sustaining  it,  or  of 
something  which  may  be  mistaken  for  it.     This 


FALLACIES  193 

might  well  be  termed  Ignoratio  or  Mutatio  con- 
du&ionis.  Formally  the  fault  is  either  in  estab- 
lishing something  that  is  not  the  required  contra- 
dictory of  the  thesis,  or  else  establishing  something 
that  is  not  the  required  thesis. 

§  145.  Consequens  is  to  infer  that  the  conclu- 
sion is  false  because  a  premise  is  false,  or  the  argu- 
ment unsound ;  also,  to  infer  the  truth  of  a  premise 
from  that  of  the  conclusion.  Thus,  if  some  one 
argues  for  the  existence  of  a  God  from  its  being 
universally  believed,  another  may  perhaps  be  able 
to  refute  the  argument  by  producing  an  instance 
of  a  nation  destitute  of  such  belief,  thus  contra- 
dicting the  minor  premise ;  the  argument  ought 
then  to  go  for  nothing.  But  many  think  that  this 
refutation  disproves  the  existence  of  a  God,  in 
which  they  are  guilty  of  illicit  major ;  thus : 

Whatever  is  univereally  believed  must  be  true; 
The  existence  of  a  God  is  not  universally  believed; 
.•.  The  existence  of  a  God  is  not  true. 

Others,  again,  from  being  already  convinced  of  the 
truth  of  the  first  conclusion,  the  existence  of  a  God, 
would  infer  the  truth  of  the  premise,  which  would 
be  the  fallacy  of  undistributed  middle ;  thus : 

What  is  universally  believed  is  true ; 
The  existence  of  a  God  is  true; 
/.The  existence  of  a  God  is  universally  believed. 

If  these  two  fallacies  be  put  in  hypothetical  form, 
the  one  shall  proceed  from  the  denial  of  the  ante- 
cedent to  the  denial  of  the  consequent ;  the  other 
18 


194  DEDUCTION 

from  aifirming  the  consequent  to  the  affirmation 
of  the  antecedent  (§§  91,  119).  These  two  condi- 
tional fallacies,  therefore,  are  thus  identified  respec- 
tively with  those  of  illicit  process  and  undistrib- 
uted middle. 

§  146.  Petitio  principii,  or  petition,  or  begging 
the  question,  is  the  assumption,  as  a  ground  of 
proof,  of  a  proposition  that  is  not  proved,  or  not 
granted,  or  not  self-evident.  It  may  occur  in  any 
one  of  five  ways  : 

1st.  "When  the  question  itself,  the  qucesitum,  the 
very  thing  to  be  proved,  is  assumed.  This  may  be 
concealed  by  using  synonyms,  or  a  name  and  its 
definition,  either  directly,  or  in  a  circumlocution. 
Thus  there  are  two  varieties. 

Hysteron  proteron,  or  the  last  first,  does  not  ex- 
tend beyond  an  epithet  or  a  single  proposition  or 
inference.  Thus:  rebel,  or  higot  Thus,  synony- 
mously :  The  doctrine  is  heretical,  for  has  it  not, 
I  heg,  caused  a  schism  in  the  Church  ?     Again : 

A  rectilinear  figure  of  three  sides  has  its  angles  equal  to  two 

right  angles; 
A  triangle  is  a  rectilinear  figure  of  three  sides; 
.'.  A  triangle  has  its  angles  equal  to  two  right  angles. 

Here  the  minor  premise  is  a  name  and  its  defini- 
tion. These  being  strictly  identical  notions  (§  35), 
differ,  not  in  thought,  but  only  in  words ;  therefore 
the  conclusion  is  assumed,  or  the  question  is  begged 
by  the  major  premise  (§  130).  The  formal  fault 
of  hysteron  proteron,  when  syllogistic,  is  that  there 


FALLACIES  195 

are  but  two  terms — a  logical  biped  (§  94).     Typi- 
cal forms  are : 

A  is  B  B  is  B 

A  is  A  and  A  is  B 

.-.A  is  B  .-.A  is  B 

The  conclusion  is  already  in  a  premise,  and  nothing 
is  proved.    Cf.  §  95,  Ex.  12 ;  and  §  131  near  end. 

Diallelon,  or  a  logical  circle,  occurs  when  u  prem- 
ise is  repeated  in  a  more  remote  conclusion.  The 
form  may  be  represented  as  a  pro-  and  epi-syllo- 
gism,  thus : 

A  is  B  C  is  B 

A  is  C  then  A  is  C 

.-.CisB  .'.AisB 

In  this  case  the  pro-syllogism  has  an  illicit  process, 
or  else  the  epi-syllogism  an  undistributed  middle. 
Of  course  any  number  of  syllogisms,  or  a  hiatus, 
may  intervene,  and  more  effectually  conceal  the  fal- 
lacy. Plato,  in  the  "  Pha^do,"  proves  the  immortal- 
ity of  the  soul  from  its  simplicity,  and,  in  the  "  Re- 
public," proves  its  simplicity  from  its  immortality. 
2d.  When  a  particular  is  to  be  proved  and  a  uni- 
versal is  assumed  without  warrant.  Thus :  The 
king  is  tyrannical^  for  are  not  all  kings  more  or 
less  so?  This  is  not  properly  a  fallacy,  for  the 
form  is  faultless  (§  133).  Yet  the  major  premise, 
being  unproven,  begs  the  question.  It  would  be 
petitio  principii  to  prove  to  a  Mohammedan  the 
divinity  of  Christ  from  New  Testament  texts,  for 
he  does  not  admit  the  authority  of  the  Bible ;  but 
it  would  be  a  valid  argumentum  ad  hominem  (§  108) 


196  DEDUCTION 

to  prove  to  him  from  the  Koran  the  prophetic 
mission  of  Jesus,  for  the  authority  of  the  Koran 
he  acknowledges. 

3d.  When  a  universal  is  to  be  proved  and  a  par- 
ticular contained  under  it  is  assumed.  Thus :  The 
knowledge  of  contraries  is  one, /or  is  not  the  knowl- 
edge of  black  and  white  (or  good  and  evil,  or  any 
other  pair  of  particular  contraries)  one  and  the 
same?  This  begs  the  question,  but  only  in  part. 
A  deduction  to  all  would  be  the  illicit  process  (§  79). 

4th.  When  the  problem  to  be  proved  is  divided 
and  its  parts  assumed  in  detail.  Thus :  Medicine 
is  the  science  of  health  and  disease.  For  is  it  not 
the  science  of  health  ?     And  also  of  disease  ? 

5th.  When  two  facts  are  reciprocally  implicated, 
and  one  is  assumed  to  prove  the  other.  Correla- 
tives imply  and  are  not  inferred  from  each  other 
(§  78).  Thus  it  is  petition  to  say :  Alexander  was 
the  son  of  Philip,  and  therefore  Philip  was  the 
father  of  Alexander;  or,  A  spark  caused  the  ex- 
plosion, therefore  the  explosion  was  caused  hy  a 
spark;  or, — therefore  the  explosion  wa^  the  effect  of 
a  spark. 

%  147.  Non  causa  pro  causa  assumes  a  premise 
which  is  not  the  cause  to  be  the  cause  of  an  absurd 
conclusion.  The  conclusion  may  be  a  proper  se- 
quence, and  its  absurdity  justify  the  contradiction 
of  a  premise,  but  not  of  the  one  assumed.  Thus : 
If  the  prisoner  was  one  of  the  burglars,  and  made 
the  foot-tracks  under  the  window,  then  he  was  wear- 


QAoOn^»^  L- cx^^^v^jjuo/ 


FALLACIES  197 

ing  shoes  half  the  size  of  his  feet  /  Imt  this  is  im- 
possible,' therefore  he  was  not  one  of  the  hurglars. 
This  reductio  ad  ahsurdum  (§  108)  authorizes  the 
denial  of  the  second  part  of  the  protasis,  but  not 
of  the  first,  with  which  the  conclusion  is  not  con- 
nected by  any  middle  term,  and  so  with  the  first 
part  makes  a  quaternion.  To  detect  the  fallacy, 
examine  whether  the  suppression  of  the  contra- 
dicted premise  would  invalidate  the  sequence. 

Evidently  this  sophism  relates  to  causa  cogno- 
scendi,  or  reason  only,  not  at  all  to  causa  essendi 
(§  110).     But  treatises  on  logic  quite  commonly 
ignore  the  true  sense,  though  the  fallacy  is  by  no 
means  rare,  and,  misled  by  the  usics  loquendi  of 
cause,  say  that  it  is  "  to  mistake  for  a  cause  what 
is  not  a  cause,"  meaning  causa  essendi.    Thus :  A  \ 
change  of  the  moon  causes  a  change  in  the  weather;/ 
Cometa  fulsit,  ergo  helium  erit.     This  fallacy  is  the) 
Cum  hoc,  vel  j?Mi  Aoc^  ergo  jrropter  hoc.     It  is  an 
important  fallacy  of  induction,  but  has  no  place  in) 


deduction. 


>^^^-_o 


§  148.  Plures  interrogationes  is  the  call  for  a 
single  answer  to  plural  questions  asked  in  one. 
Thus :  Was  Pisistratus  the  tyrant  and  scourge  of 
Athens?  As  he  was  the  one  but  not  the  other, 
either  a  yea  or  a  nay  would  commit  the  respondent 
to  a  false  position.  Avoiding  one  horn,  he  is  caught 
on  the  other,"  and  hence  this  sophism  is  sometimes 
called  the  Cornutus.  A  safe  answer  is.  Yes  and  no. 
A  variation  in  form  is :  Are  you  the  only  rogue  in 


198  DEDTJCTION 

your  family  ?  Such  forms  are  much  used  in  teasing, 
and  lawyers  badger  unsophisticated  witnesses  in  this 
way.  To  some  compound  question  they  demand 
what  they  call  "  a  categorical  answer,"  meaning  a 
simple  yea  or  nay,  when  either  will  entrap  the  wit- 
ness in  a  damaging  admission,  or  in  a  self-contra- 
diction or  other  falsity.  Again  :  Why  is  a  violin- 
cello  player  always  fat  ?  But  we  should  inquire 
an  sit?  before  cur  sit?  The  ancient  example. 
Have  yon  cast  your  horris  ?  may  be  stated  :  Either 
you  have  cast  your  ho7'ns,  or  you  have  them  still,' 
which  ?  But  there  is  a  tertium  omitted :  or  you 
have  never  had  ho?ms.  In  this  case  it  is  the  fallacy 
of  incomplete  disjunction  (§  114).  All  this  seems 
quite  frivolous,  but  it  is  not  always  so.  Nor  is  the 
form  necessarily  fallacious.  It  is  used  b}'^  our  Lord 
to  entangle  his  adversaries  (Matt.  xxi.  24-27),  in 
which  case  the  disjunction  is  complete. 

§  149.  Praxis.  Designate  and  describe  the  par- 
alogisms occurring  in  many,  yet  not  in  every  one, 
of  the  following  examples : 

1.  All  plants  come  from  seed,  therefore  all  seeds  come 

from  plants.  ^1  - 

2.  The  French  Academy  defined  a  crab  as  a  small 

red  fish  that  walks  backwards.  Very  good,  said 
Cuvier,  only  a  crab  is  not  a  fish,  is  not  red,  and 
does  not  walk  backwards. 

3.  A  legitimate  argument  may  fail  to  Win  assent ; 

No  fallacy  is  a  legitimate  argument;  * 

.*.  No  fallacy  can  fail  to  win  assent. 


h 


FALLACIES  199 

4.  A  monse  is  an  animal,  therefore  (by  determination, 

§  80)  a  very  large  mouse  is  a  very  large  animal. 

5.  Evorv  one  desires  happiness  :  but  virtue  secures  -,     _ 

•     .  rr  '  (1     ^ 

happiness ;  therefore  every  one  desires  virtue.      <^     \^ 

6.  Only  give  me  the  luxuries  of  life,  and  I  will  dis- 

pense with  the  necessaries. 

7.  None  but   whites  are  civilized ;  the  ancient  Ger-       1?        ' 

mans  were  whites;  hence  they  were  civilized.  ^—^ 

8.  None  but  whites  are  civilized ;  the  East  Indians      'W 

are  not  whites ;  hence  they  are  not  civilized.  j 

9.  No  eood  doctor  ever  takes  fees ;  all  good  doctors  ,'^' 

are  also  lawyers;  hence  lawyers  never  take  fees.     (Tul^hZ^ 

10.  A  little  girl  studying  arithmetic,  and  coming  to  a 

"  sura "  in  which  oranges  were  exchanged  for 
eggs,  refused  to  try  it,  saying  nobody  would  be 
such  a  fool.         fCj     ^^    ^  '   ^  ^    '^  y 

1 1.  J.  S.  Mill's  introduction  to  his  "  Political  Economy  " 

is  entitled  "  Preliminary  Remarks,"  which  pro- 
poses a  prospective  review.  I    ^ 

12.  A  spaniel  is  defined  as  a  species  of  the  proximate 

genus  dog.  ■  -^ 

13.  Can  you  mention  anything  that  is  coijunon  prop- 

erty  ? 

14.  All  that  glitters  is  not  gold;  tinsel  glitters;  there- 

fore tinsel  is  not  gold.  , 

15.  Never  do  anything  you  need  to  be  ashamed  of,  and 

then  you  need  never  be  ashamed  of  anything 
you  do. 

16.  All  do  not  strive ;  but  all  wish  to  "succeed ;  hence 

not  all  strive  who  wish  to  succeed.    . 

17.  Some  possible  cases  are  improbable  ; 
.'.  Some  probable  cases  are  impossible. 


\ 


200  DEDUCTION 

-  a /^- '■'*''' ^  _ 

■^    18.  Liberty  is  a  negation  (absence  of  constraint); 
We  cannot  be  conscious  of  a  negative ; 
.-.  We  cannot  be  conscious  of  liberty, 
19.  Shakespeare  knew  little  Latin  and  less  Greek. 
2©.  Touchstone   says   to   Corin  :   Why,  if  thou    never 
wast  at  court,  thou  never  saw'st  good  manners ; 
if   thou    never   saw'st   good   manners,  then    thy 
manners  must  be  wicked  ;  and  wickedness  is  sin, 
and  sin  is  damnation.      Thou  art  in  a  parlous 
state,  Shepherd !    ' 

21.  If  some  men  are  strong,  it  follows  that  some  are  weak.\^. 

22.  An  agnostic  is  one  who  holds  that  it  is  impossible 

to  know  anything  with  certainty.       1^  "^ 

23.  There  is  no  rule  without  exceptions ; 
This  statement  is  itself  a  rule  ; 

.*.  This  statement  has  exceptions,  or  'L-      j 

There  are  rules  without  exceptions. 

24.  If  a  wife  be  beautiful,  she  excites  jealousy ; 
If  she  be  ugly,  she  excites  disgust ;  x j  [ji 
Therefore  it  is  best  not  to  marry. 

25.  Whatever  represses  the  liberties  of  mankind  ought 

to  be  resisted ;  but  among  the  things  that  do  so, 
there  are  governments ; 
.*.  Governments  ought  to  be  resisted. 

26.  Nothing  is  better  than  wisdom  ;  /^ 
Dry  bread  is  better  than  nothing; 

/.  Dry  bread  is  better  than  wisdom. 

27.  Those  to  whom  the  Gospel  promises  come  are  the 

faithful ; 
Many  whom  the  world  condemns  are  faithful ; 
.*.  The    Gospel  promises   come   to   many  whom  the 
world  condemns. 


FALLACIS8  201 

Designate  and  describe  the  sophisms  in  diction 
occurring  in  many  of  the  following  examples : 

28.  Whoever  necessarily  goes  or  stays  is  not  a  free  agent ; 
But  every  one  necessarily  either  goes  or  stays ; 

.'.  No  one  is  free. 

29.  Whatever  a  man  walks  on  he  tramples  on ; 
This  man  walks  on  the  whole  day  ; 

.-.  He  tramples  on  the  day. 

30.  The  prophet  spake  to  his  sons,  saying,  Saddle  me 

the  ass ;  and  they  saddled  him. 

31.  All  criminal  actions  should  be  punished  by  law  ; 
Prosecutions  for  theft  are  criminal  actions ; 

.'.  Prosecutions  for  theft  should  be  punished  by  law. 

32.  No  moral  principle  is  an  animal  impulse ; 

But  some  animal  impulses  are  principles  of  action ; 
.•.  Some  principles  of  action  are  not  moral  principles. 

33.  A  member  of  Congress,  charged  with  having  called 

another  a  liar,  apologized  thus :  It  is  quite  true^        ^ 
and  I  am  sorry  for  it. 

34.  Our  consciousness  testifies  to  the  external  reality 

of  objects  of  sense-perception,  but  is  its  witness  -^     ' 
true  ?   Of  course,  for  your  assertion,  literally  taken, 
means  only  this,  that  we  are  conscious  of  external 
reality. — A  reply  to  Hamilton. 
36.  Thou    shalt   not   bear    false    witness    against   thy 
neighbor. 

36.  The  planets  are  seven  ;   Mercury  and   Venus  are 

planets ; 
.*.  Mercury  and  Venus  are  seven. 

37.  Finis  rei  est  illius  perfectio ; 
Mors  est  finis  vitse  ; 

.•.  Mors  est  vitse  perfectio. 


202    .  DEDUCTION 

(T     38.  Either  animal  or  vegetable  food  may  be  altogether 
dispensed  with ; 
All  food  is  either  animal  or  vegetable ; 
:.  All  food  may  be  altogether  dispensed  with. 

39.  Philip  saith  to  the  eunuch,  Fu'wo-ivetc  ci  avayLvitaKUQ  ; 

40.  Pilate  saith  to  the  Jews,  Behold  your  King ! 
And  they  cried,  Hail,  King  of  the  Jews ! 

Designate  and  describe  the  sophisms  in  matter 
occurring  in  many  of  tlie  following  examples : 

4' .  The  gods,  say  the  Epicureans,  must  be  invested  with 
the  human  form,  because  this  form  is  most  beau- 
'  tiful ;  and  everything  beautiful  must  be  found  in 

them. 
42.  To  pray  for  rain  is  to  ask  for  a  miracle ;  but  mira- 
cles have  ceased.     It  is  replied,  first,  that  prayer 
for  rain  has  often  been  followed  by  rain  ;  secondly, 
that  men  have  succeeded  in  causing  rain,  and  to 
say  God  cannot  do  what  men  can  do  is  impious. 
^     43.  Prayer  may  be  regarded  as  useful,  if,  indeed,  we 
can  regard  our  prayers  as  announcing  to  Deity 
what  he  does  not  know,  or  as  effectual  in  chang- 
ing his  purposes  ;     ^o.—  ^C   —  ^'t   ^  '^  :,^  ~ 
But  we  cannot  tell  the  Omniscient  wnat  he  does 
not  already  know,  nor  effect  a  change  in  his  e_ter- 
nal  purposes;      ^  _^       c^  a  '  ^  / 
.*.  Prayer  is  useless. 

44.  The  right  of  the  government  to  command  is  un- 

questionable ;  therefore  we  aught  to  obey  it. 

45.  IJnless  logic  profess  to  be  an  instrument  of  inven- 
f  tion,  the  reproach   that  it   discovers  nothing  is 

unfounded ;  but  it  does  not  make  this  profes- 
sion, and  hence  this  reproach  is  unfounded. 


*>^" —  FALLAOIBS  203 

46.  Either  God  wills  to  remove  evils  and  cannot;  or 

he  can  and  will  not ;  or  he  neither  will  nor  can ; . 
or  he  both  will  and  can.  If  he  will  and  cannot, 
then  he  is  weak,  which  is  not  true  of  God.  If 
he  can  and  will  not,  then  he  is  malicious,  which 
also  is  foreign  to  the  nature  of  God.  If  he  nei- 
ther will  nor  can,  then  he  is  both  malicious  and 
weak,  and  therefore  cannot  be  God.  If  he  both 
can  and  will,  which  alone  is  consistent  with  the 
nature  of  God,  then  whence  are  evils,  or  why 
does  he  not  remove  them  ? 

47.  To  allow  every  man  freedom  of  speech  must  always 

be,  on  the  whole,  for  the  good  of  the  state  ;  for 
it  is  highly  conducive  to  the  interests  of  the 
community  that  each  individual  should  enjoy  a 
liberty,  perfectly  unlimited,  of  expressing  his 
sentiments  on  its  affairs. 

48.  Mental  effort  promotes  intellectual  vigor,  but  wearies    }?^ 

the  brain  ;  hence  what  wearies  strengthens ;  but 
hard  study  is  wearisome,  and  therefore  strength- 
ens the  mind. 

49.  Whatever  is  true'  of  John,  Peter,  etc.,  is  true  of  all 

mankind ; 
Mortality  is  true  of  John,  Peter,  etc. ; 
.*.  Mortality  is  true  of  all  mankind. 

—  Whately^s  "  inductive  syllogism,''^  approved 
as  such  by  Mill,  Logic,  bk.  iii.,  ch.  iii. 

50.  This,  that,  and  the  other  magnet  attract  iron ; 
This,   that,    and   the    other   magnet   represent   all 

magnets ; 
.*.  All  magnets  attract  iron. 

— Hamilton's  "  inductive  syllogism,''^  Logic,  §  62. 


204  DEDUCTION 

61.  What  is  not  an  uncommon  occurrence  may  reason- 
ably be  expected ; 
To  gain  a  high  prize  in  a  lottery  is  not  an  uncom- 
mon occurrence ; 
.*.  To  gain  a  high  prize  in  a  lottery  may  reasonably 
be  expected. 
52.  He  who  calls  you  a  man  speaks  truly ; 

He  who  calls  you  a  knave  calls  you  a  man ; 
.-.  He  who  calls  you  a  knave  speaks  truly. 

63.  Every  effect  is  caused  ; 
The  world  is  an  effect ; 

.-.  The  world  is  caused. 

64.  Why  does  a  ball,  when  dropped  from  the  mast-head 

of  a  ship  in  full  sail,  fall  not  exactly  at  the  foot 
of  the  mast,  but  nearer  to  the  stern  of  the  vessel  ? 
66.  Who  is  most  hungry  eats  most ; 
Who  eats  least  is  most  hungry ; 
/,  Who  eats  least  eats  most. 
66.  Omne  animal  rationale  est  risibile ; 
Omnis  homo  est  animal  rationale ; 
.*.  Omnis  homo  est  risibilis, 
57.  We  are  forbidden  to  kill ; 

Inflicting  capital  punishment  is  killing; 
.'.  We  are  forbidden  to  inflict  capital  punishment. 
68.  He  that  is  of  God  heareth  the  words  of  God :  for 
this  cause  ye  hear  them  not,  because  ye  are  not 
of  God. — John  viii.  47. 


'<L^s 


X^ 


INDEX 


( Tlie  number  refers  to  the  page.) 


Abstraction,  its  process,  15. 
Accentus,  prosodia,  fallacy  of,  188. 
Accidens,  conversion  per,  92. 

—  fallacy  of,  190. 
Accident,  the  mark,  16,  44. 
^quivocatio,  fallacy  of,  185. 

Am biguity  of  aWaiid  of  some,  73, 74. 
Ambiguous  terms,  fallacies  of,  185. 
Ampliibolia,  fallacy  of,  186. 
Analysis  of  conjunctives,  153,  165. 
Antecedents,  affirmed   or  denied, 

109. 
Argumentum  ad  rem,  139. 

—  a  fortiori,  140,  179. 

—  ad  verecundiam,  140. 

—  ad  judicium,  140. 

—  ad  populum,  140. 

—  ad  absurdum,  impossibile,  11, 
141. 

—  ad  hominem,  141. 
Aristotle,  categories  of,  63. 

—  predicables  of,  64. 

Art  distinguished  from  science,  2. 
Axioms  of  iiiequahty,  173, 178, 179. 

—  of  reason  and  conseq.,  109,  159. 

Begging  the  question,  forms  of,l  94. 
Biped,  the  logical,  195.  *> 

Bulls,  self-contradiction,  186. 

Canon  of  mediate  inference.  111, 
176. 

—  of  replacement,  112. 

—  of  immediate  inference,  174. 

—  of  partitive  syllogisms,  178. 

—  of  comparative  syllogisms,  1 79. 


Categorical  propositions,  67. 
Categories  or  predicaments,  fl8. 
Causae,  essendi,  cognoscendi,  14<s 

197. 
Circle,  the  logical,  195. 
Circular  notation,  29,  100,  136. 

—  criticised,  102. 
Classification,  18. 
Clauses,  of  two  kinds,  76. 
Clearness  and  distinctness,  28. 
Coextensive  notions,  29,  30. 
Collective  whole,  26,  28. 
Comparative  syllogisms,  179. 
Complex  propositions,  76. 
Com positio,  fallacy  of,  187. 
Compound  propositions,  79. 
Concept  and  mark  commutabie,  20 
Conception,  its  modes,  18. 
Concrete  and  abstract  terms,  17. 
Conditio  sine  qua  non,  146,  169. 
Condition,  its  kinds,  146. 
Conditional  propositions,  67,  148. 

—  syllogisms,  158. 

—  analyzed  and  criticised,  165. 
Congruent  notions,  29. 
Conjunctive  propositions,  148. 

—  analysis  of,  153. 

—  syllogisms,  160. 
Conjunctivo-disjunctives,  162. 

—  syllogisms,  163. 
Connotation  and  denotation,  20, 22. 
Consequens,  fallacy  of,  108,  169, 

193. 
Consequents,  affirmed  or  denied, 

109. 
Contradiction,  law  of,  9, 69,  60, 94 


206 


INDEX 


Contradiction,  rule  for,  94. 
Contraposition,  93. 
Contrariety,  36,  95, 151. 
Conversion,  inference  by,  91. 
Co-ordination  of  notions,  30,  33. 
Copula,  liow  qualified,  69. 
Copulative  proposition,  151. 

—  syllogism,  162. 
Cornutus,  fallacy  of,  19*7. 
Correlation  not  inference,  196. 
Correlative  notions,  34,  89. 
Cross  division,  test  of,  39. 

Deductive  inference,  88. 
Definition  of  logic,  1. 

—  of  science,  1. 

—  of  marks,  17. 

—  of  concept,  18,  20. 

—  of  individual,  27. 

—  constituents  of,  41. 

—  a  priori  and  real,  44. 

—  a  posteriori,  44. 

—  nominal,  45. 

—  genetic  or  causal,  45. 

—  rules  for,  45. 

—  correlated  with  division,  54. 
Denotation  and   connotation,  20, 

22. 
Determination,  inference  by,  90. 
Diallelon,  the  circle,  195. 
Dichotomy,  division  by,  33. 
Dicta  de  omni  et  nuUo,  111. 
Dilemma,  its  forms,  163. 
Dilemmatic  propositions,  152. 
Disjunctive  propositions,  149. 

—  syllogisms,  161. 
Disparate  notions,  36,  150. 
Distinctness,  two  modes  of,  24. 
Divisio,  fallacy  of,  187. 
Division  by  dichotomy,  33. 

—  ground  of,  36. 

—  kinds  of,  37. 

—  rules  for,  38. 

—  correlated  with  definition,  54 

Enthymeme,  four  orders  of,  132. 
Epichirema,  analyzed,  134. 
EquipoUence,  14. 
Exclusives  and  exceptives,  80. 
Existential  forms,  60, 148. 


Exponible  propositions,  79. 
Extension  and  intension,  law  o^ 
22. 

—  illustrated,  49,  62. 

Fallacies,  distribution  of,  184. 

—  in  diction,  185. 

—  in  matter,  190. 

False  matter  not  fallacy,  183. 
Figura  dictionis,  fallacy  of,  189. 
Figures,  the  four,  120. 
Form  and  matter  distin<riiislie(l,4. 
Fourth  figure  criticised,  128. 
Fundamentum  divisionis,  36. 

General  rules  of  syllogism,  114. 
Generalization,  process  of,  17. 
Genetic  or  causal  definition,  45. 
Genus  and  species,  31,  33. 
Geometrical  illustration,  177. 
Graphic  notation,  103, 135. 
Ground  of  division,  36. 

Hypothetical  propositions,  148. 

—  syllogisms,  160. 

Hysteron  proteron,  fallacy  of,  194. 

Ignoratio  elenchi,  fallacy  of,  192. 
Illicit  process,  90. 

—  major  and  minor,  116. 
Implications  not  inferences,  88. 
Incongruent  notions,  28. 
Indefinable  notions,  42. 
Indefinite  propositions,  73. 
Individual  propositions,  72. 
Individuals,  concepts  of,  19,  27. 

—  indefinable,  42. 

—  how  related  to  system,  52. 

—  as  predicates,  63,  174. 
Inference  defined  and  divided,  87. 
Iiifima  species,  61. 
Infiiritation,  inference  by,  91. 
Infinite  propositions,  62. 
Integral  whole,  26,  28. 
Intension  and  extension,  law  o^ 

22. 

—  illustrations  of,  49. 

—  predication  of,  62. 

—  syllogisms  of,  99,  104. 

—  differences  estimated,  106. 


INDEX 


207 


Intentions,  first  and  second,  4. 
Intersection  of  notions,  80,  39, 42. 

Judgment,  defined,  6*7. 

—  distributed,  87, 147. 

—  the  syllogistic,  107. 

Law  of  identity,  9,  59,  60. 

—  of  contradiction,  9,  59,  60,  94. 

—  of  excluded  middle,  11,  59,  60. 

—  of  intension  and  extension,  23. 
Linear  notation,  29,  100,  136. 

—  criticised,  102. 
Logic,  definition  of,  1. 

—  a  science,  not  an  art,  2. 

—  an  abstract  science,  5. 

—  a  fundamental  science,  5. 

—  a  negative  criterion,  12. 

—  a  postulate  of,  13. 

Logical  or  qualitative  whole,  26,28. 

—  partition  or  section,  28. 

—  division,  83. 

—  definition,  43. 

—  tree  or  ladder,  56. 

Many  questions,  fallacy  of,  197. 
Marks,  kinds  of,  15. 

—  definition  of,  17. 

—  and  concepts  commutable,  20. 
Material  fallacies,  190. 
Mathematical  whole,  26,  27, 171. 

—  syllogisms,  175,  177. 
Matter  and  form,  4,  8,  50. 
Mediate  inference,  88. 
Mnemonic  hexameters,  124. 
Moods,  how  ascertained,  123. 
Mutatio  conclusionis,  198. 

Necessity  of  logical  form,  5. 

—  in  what  sense  violable,  6, 188 
Negative  species,  34,  36. 

—  predication,  61,  70. 
Nominal  definition,  45 

Non  causa  pro  causa,  fallacy  of, 

196. 
Notations,  29, 100,  122, 185. 

—  geometric  criticised,  102. 

—  graphic  explained,  103. 
Notions,individual  and  general,  18. 
Nouns,  common  and  proper,  21. 


Onus  proband!,  142. 
Opposition,  inference  by,  94,  96. 
Oracles,  the  trick  of,  187. 
Order,  strict  logical,  70. 
Ostensive  reduction,  126. 

Paradox,  logical,  rhetorical,  10, 11. 
Paralogism,  184. 
Paranomasia  or  pun,  186. 
Paronyms,  fallacy  of,  190. 
Particular  propositions,  73. 
Partitive  syllogisms,  178. 
Per  accidens,  conversion,  92. 
Petitio  principii,  fallacy  of,  194. 
Plures  interrogaliones,  fallacy  of, 

197. 
Polytomy,  its  origin,  85. 
Porphyry's  tree,  56. 
Postulate  of  logic,  13. 
Predesignations  of  quantity,  73, 74 
Predicables  of  Aristotle,  64. 
Predicaments  or  categories,  68. 
Predicates,  quantification  of,  82 

—  rule  for  distribution  of,  85. 
Predication,  its  limits,  59. 

—  of  existence,  60. 

—  of  negative  notions,  61. 
Premises,  definition  of,  101. 
Primary  laws,  8,  59,  60. 

—  reduction  to  unity  of,  12 
Privative  notions,  36. 
Propositions,  existential,  6C 

—  negative,  61. 

—  infinite,  62. 

—  definition  of,  67 

—  logical  parts  of,  68. 

—  distribution  of,  71, 147. 

—  individual,  72. 

—  universal,  72. 

—  particular  or  indefinite,  7c 

—  simple,  scheme  of,  76. 

—  symbols  of,  75,  83 

—  conditional,  146. 

—  of  equality  and  inequality,  172. 
Prosodia,  accentus,  fallacy  of,  188. 
Proximate  genus,  43. 
Punctuation,  fallacy  of,  188. 
Punning,  fallacy  of,  186. 

Quadruped,  the  logical,  114, 186 


208 


INDEX 


Qualitative  whole,  26,  28. 
Quantified  predicates,  82. 

—  symbol3  of,  83. 
Quantitative  whole,  26,  27, 171. 

—  propositions,  171. 

—  syllogisms,  175. 
Quaternions,  114, 185. 

Reason  and  consequent,  147. 

—  axioms  of,  109, 159. 
Reasoning,  88,  99,  100,  107,  132. 

■ —  conditional  forms  of,  164,  158 

—  criticism  of,  165. 

—  quantitative  forms  of,  175, 178. 
Reductio  ad  absurdum,  11, 141. 
Reduction  of  syllogisms,  125. 

—  ad  impossible,  127. 
Replacement,  canon  of,  112. 
Rhetorical  identity,  9. 

—  contradiction,  11. 

—  inversions,  71 

Rule    for    distribution    of    predi- 
cates, 85. 

—  for  quantity  inferred,  89. 

—  for  infinitation,  91, 

—  for  contraposition,  93. 

—  for  contradictory  oppos.,  94. 

—  for  contrary  opposition,  95. 

—  for  subcontrary  opposition,  96, 

—  for  subalternate  opposition,  96. 

—  for  intensive  syllogism,  105. 

—  for  reduction,  general,  127. 
Rules  for  division,  38. 

—  for  definition,  45. 

—  for  syllogism,  general,  114. 

—  for  syllogism,  special,  121. 

—  for  syllogism,  conjunctive,  160. 

Science,  definition  of,  1. 
Secundum  quid,  fallacy  of,  191 
Self-contradiction,  186. 
Semi-definite  some,  75,  81,  89, 
Signs  of  quantity,  73. 
Simple  notions  indefinable,  42. 
Some,  ambiguity  of,  74. 


Some,  semi-definite,  75,  81,  89. 
Sophisms  in  diction,  186. 

—  in  matter,  190. 
Sorites,  scheme  of,  136. 
Special  rules  for  syllogism,  121, 
Specialization,  process  of,  18. 
Species  and  genus,  31,  33. 
Specific  difference,  43. 
Square  of  opposition,  94. 
Subalternate  opposition,  96. 
Subcontrary  opposition,  96. 

—  propositions,  151. 

—  syllogisms,  162. 
Subordinate  notions,  29,  30. 
Summum  genus,  50. 
Syllogism,  definition  of,  100.    ■ 

—  necessity  of,  107. 

—  truth  and  falsity  of,  108. 

—  conditional  forms  of,  108, 161 

—  compound,  136. 

—  disguised,  137. 

—  conjunctive,  160. 

—  disjunctive,  161. 

—  copulative,  162. 

—  analyzed  and  criticised,  166 

—  of  equivalence,  175. 

—  partitive,  178. 

—  comparative,  179. 
Symbols  of  propositions,  76,  85^ 

Terms,  definition  of,  101. 
Thought,  the  matter  of  logic,  8 
Tree,  the  logical,  56. 
Trichotomy,  its  origin,  36. 
True  and  false  matter,  108, 18o 

Ultra-total  quantification,  116. 
Undistributed  middle,  116. 
Universe,  the  logical,  10,  31. 
Universal  propositions,  72. 

Violation  of  logical  law,  13, 18& 

Wholes,  of  two  kinds,  26. 
Words,  signs  of  thoughts,  20. 


FINIS 


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DaviSi     Noah    KnowleSi     1830-1910. 

Elements  of  deductive  logic.  By  Noah 

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